메뉴 건너뛰기




Volumn 25, Issue 3-4, 1997, Pages 569-595

Fully Nonlinear Second Order Elliptic Equations: Recent Development

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0007384467     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (31)

References (100)
  • 2
    • 85129394802 scopus 로고
    • Research into maximum principle. VI, Izvestiya Vysshikh Uchebnykh Zavedenii
    • Russian
    • A. D. ALEKSANDROV, Research into maximum principle. VI, Izvestiya Vysshikh Uchebnykh Zavedenii, Ser. Math. No. 1 (1961), 3-20 in Russian.
    • (1961) Ser. Math , Issue.1 , pp. 3-20
    • ALEKSANDROV, A. D.1
  • 3
    • 85129426035 scopus 로고    scopus 로고
    • Uniqueness conditions and estimates for solutions of the Dirichlet problem, Vestnik Leningrad. Univ., Vol. 18, No. 3 (1963), 5-29
    • English translation in Amer. Math. Soc. Transl. (2) 68 (1968), 89-119
    • A. D. ALEKSANDROV, Uniqueness conditions and estimates for solutions of the Dirichlet problem, Vestnik Leningrad. Univ., Vol. 18, No. 3 (1963), 5-29. English translation in Amer. Math. Soc. Transl. (2) Vol. 68 ( 1968), 89-119.
    • ALEKSANDROV, A. D.1
  • 5
    • 85129408448 scopus 로고
    • Control of a diffusion process in a region with fixed reflection on the boundary
    • Steklov Seminars 1985-86, Optimization Software Inc., New York
    • S. V. ANULOVA - M. V. SAFONOV, Control of a diffusion process in a region with fixed reflection on the boundary, pp. 1-15 in "Statistics and Controlled Stoch. Processes", Steklov Seminars 1985-86, Vol. 2, Optimization Software Inc., New York, 1989.
    • (1989) Statistics and Controlled Stoch. Processes , vol.2 , pp. 1-15
    • ANULOVA, S. V.1    SAFONOV, M. V.2
  • 7
    • 84974753170 scopus 로고
    • Convergence of approximation schemes for fully nonlinear second order equations
    • G. BARLES - P. E. SOUGANIDIS, Convergence of approximation schemes for fully nonlinear second order equations, Asymp. Anal., Vol. 4, No. 3 (1991), 271-283.
    • (1991) Asymp. Anal , vol.4 , Issue.3 , pp. 271-283
    • BARLES, G.1    SOUGANIDIS, P. E.2
  • 8
    • 0002098825 scopus 로고
    • Sur la generalization du problems de Dirichlet. (Deuxième partie)
    • S. BERNSTEIN, Sur la generalization du problems de Dirichlet. (Deuxième partie), Math. Annalen., Vol. 69 (1910), 82-136.
    • (1910) Math. Annalen , vol.69 , pp. 82-136
    • BERNSTEIN, S.1
  • 9
    • 0000898166 scopus 로고
    • Interior a priori estimates for solutions of fully nonlinear equations
    • L. A. CAFFARELL, Interior a priori estimates for solutions of fully nonlinear equations, Annals of Math.130 No. 1 (1989), 189-213.
    • (1989) Annals of Math , vol.130 , Issue.1 , pp. 189-213
    • CAFFARELL, L. A.1
  • 10
    • 0002068394 scopus 로고
    • Interior W2,p -estimates for solutions of the Monge-Ampère equation
    • L. A. CAFFARELLI, Interior W2,p -estimates for solutions of the Monge-Ampère equation, Annals of Math. 131 No. 1 (1990), 135-150.
    • (1990) Annals of Math , vol.131 , Issue.1 , pp. 135-150
    • CAFFARELLI, L. A.1
  • 11
    • 84968482174 scopus 로고
    • The regularity of mappings with convex potentials
    • L. A. CAFFARELLI, The regularity of mappings with convex potentials, J. Amer. Math. Soc. Vol. 5 (1992), 99-104.
    • (1992) J. Amer. Math. Soc , vol.5 , pp. 99-104
    • CAFFARELLI, L. A.1
  • 12
    • 84990563964 scopus 로고
    • Boundary regularity of maps with convex potentials
    • L. A. CAFFARELLI, Boundary regularity of maps with convex potentials, Comm. Pure Appl. Math. Vol. 45 (1992), 1141-1151.
    • (1992) Comm. Pure Appl. Math , vol.45 , pp. 1141-1151
    • CAFFARELLI, L. A.1
  • 13
    • 0002449458 scopus 로고
    • Fully Nonlinear Elliptic Equations
    • American Math. Soc, Providence, R I
    • L. A. CAFFARELLI - X. CABRÉ, "Fully Nonlinear Elliptic Equations", Colloquium Publications Vol. 43, American Math. Soc, Providence, R I, 1995.
    • (1995) Colloquium Publications , vol.43
    • CAFFARELLI, L. A.1    CABRÉ, X.2
  • 14
    • 84990580987 scopus 로고
    • The Dirichlet problem for nonlinear second order elliptic equations, I. Monge-Ampère equations
    • L. CAFFARELLI - L. NIRENBERG - J. SPRUCK, The Dirichlet problem for nonlinear second order elliptic equations, I. Monge-Ampère equations, Comm. Pure Appl. Math. Vol. 37 (1984), 369-402.
    • (1984) Comm. Pure Appl. Math , vol.37 , pp. 369-402
    • CAFFARELLI, L.1    NIRENBERG, L.2    SPRUCK, J.3
  • 15
    • 84990557319 scopus 로고
    • The Dirichlet problem for nonlinear second order elliptic equations, II. Complex Monge-Ampère, and uniformly elliptic, equations
    • L. CAFFARELLI - J. J. KOHN - L. NIRENBERG - J. SPRUCK, The Dirichlet problem for nonlinear second order elliptic equations, II. Complex Monge-Ampère, and uniformly elliptic, equations, Comm. Pure Appl. Math. Vol. 38 (1985), 209-252.
    • (1985) Comm. Pure Appl. Math , vol.38 , pp. 209-252
    • CAFFARELLI, L.1    KOHN, J. J.2    NIRENBERG, L.3    SPRUCK, J.4
  • 16
    • 0000658663 scopus 로고
    • The Dirichlet problem for nonlinear second order elliptic equations, III. Functions of the eigenvalues of the Hessian
    • L. CAFFARELLI - L. NIRENBERG - J. SPRUCK, The Dirichlet problem for nonlinear second order elliptic equations, III. Functions of the eigenvalues of the Hessian, Acta Math., Vol. 155, No. 3-4 (1985), 261-301.
    • (1985) Acta Math , vol.155 , Issue.3-4 , pp. 261-301
    • CAFFARELLI, L.1    NIRENBERG, L.2    SPRUCK, J.3
  • 17
    • 0001880933 scopus 로고
    • The Dirichlet problem for the degenerate Monge-Ampère equation
    • 2
    • L. CAFFARELLI - L. NIRENBERG - J. SPRUCK, The Dirichlet problem for the degenerate Monge-Ampère equation, Revista Mat. Iberoamericana, Vol. 86, No. 1, 2 (1986), 19-27.
    • (1986) Revista Mat. Iberoamericana , vol.86 , Issue.1 , pp. 19-27
    • CAFFARELLI, L.1    NIRENBERG, L.2    SPRUCK, J.3
  • 18
    • 84990587364 scopus 로고
    • Nonlinear second order equations, IV. The Dirichlet problem for Weingarten surfaces
    • L. CAFFARELLI - L. NIRENBERG - J. SPRUCK, Nonlinear second order equations, IV. The Dirichlet problem for Weingarten surfaces, Comm. Pure Appl. Math. Vol. 41 (1988), 47-70.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 47-70
    • CAFFARELLI, L.1    NIRENBERG, L.2    SPRUCK, J.3
  • 19
    • 0000057533 scopus 로고
    • Improper affine hypersurfaces ofconvex type and a generalization ofa theorem by K. Jorgens
    • E. CALABI, Improper affine hypersurfaces ofconvex type and a generalization ofa theorem by K. Jorgens, Michigan. Math. J. Vol. 5 (1958), 2.
    • (1958) Michigan. Math. J , vol.5 , pp. 2
    • CALABI, E.1
  • 21
    • 84980170512 scopus 로고
    • On the regularity of the Monge-Ampère equation det (~2u/~xi~xj) = F(x, u)
    • S. Y. CHENG - S. T. YAU, On the regularity of the Monge-Ampère equation det (~2u/~xi~xj) = F(x, u), Comm. Pure Appl. Math. Vol. 30 (1977), 41-68.
    • (1977) Comm. Pure Appl. Math , vol.30 , pp. 41-68
    • CHENG, S. Y.1    YAU, S. T.2
  • 23
    • 84967708673 scopus 로고
    • User’s guide to viscosity solutions of second order partial differential equations
    • M. G. CRANDALL - H. ISHII - P. L. LIONS, User’s guide to viscosity solutions of second order partial differential equations, Bulletin Amer. Math. Soc. Vol. 27, No. 1 (1992), 1-67.
    • (1992) Bulletin Amer. Math. Soc , vol.27 , Issue.1 , pp. 1-67
    • CRANDALL, M. G.1    ISHII, H.2    LIONS, P. L.3
  • 24
    • 85012863369 scopus 로고
    • Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
    • P
    • P. DELANOË P., Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator, Ann. Inst. Henri Poincaré, Vol. 8, No. 5 (1991), 443-457.
    • (1991) Ann. Inst. Henri Poincaré , vol.8 , Issue.5 , pp. 443-457
    • DELANOË, P.1
  • 25
    • 84990553687 scopus 로고
    • Classical solutions offully nonlinear convex, second order elliptic equations
    • L. C. EVANS, Classical solutions offully nonlinear convex, second order elliptic equations, Comm. Pure Appl. Math., Vol. 25 (1982), 333-363.
    • (1982) Comm. Pure Appl. Math , vol.25 , pp. 333-363
    • EVANS, L. C.1
  • 26
    • 84967792520 scopus 로고
    • Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators
    • L. C. EVANS, Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators, Trans. Amer. Math. Soc., Vol. 275 (1983), 245-255.
    • (1983) Trans. Amer. Math. Soc , vol.275 , pp. 245-255
    • EVANS, L. C.1
  • 28
    • 84972495800 scopus 로고
    • Flow of nonconvex hypersurfaces into spheres
    • C. GERHARDT, Flow of nonconvex hypersurfaces into spheres, J. Diff. Geom. Vol. 32 (1990), 299-314.
    • (1990) J. Diff. Geom , vol.32 , pp. 299-314
    • GERHARDT, C.1
  • 30
    • 0001358839 scopus 로고
    • The Dirichlet problem for a class offully nonlinear elliptic equations
    • B. GuAN, The Dirichlet problem for a class offully nonlinear elliptic equations. Comm. in P D E, Vol. 19, No. 3-4 (1994), 399-416.
    • (1994) Comm. in P D E , vol.19 , Issue.3-4 , pp. 399-416
    • GuAN, B.1
  • 33
    • 0000978591 scopus 로고
    • Boundary value problem on for surfaces of constant Gauss curvature
    • B. GuAN - J. SPRUCK, Boundary value problem on for surfaces of constant Gauss curvature. Annals of Math., Vol. 138 (1993), 601-624.
    • (1993) Annals of Math , vol.138 , pp. 601-624
    • Gu, B.1    SPRUCK, J.2
  • 34
    • 33646861117 scopus 로고
    • Classical solvability of the Dirichlet problem for the Monge-Ampère equation
    • Russian. English translation in J. Soviet Math. 30 4 (1985), 2287-2292
    • N. M. IvocHKiNA, Classical solvability of the Dirichlet problem for the Monge-Ampère equation, Zapiski Nauchn. Sem. L O M I AN S S S R, Vol. 131 (1983), 72-79 in Russian. English translation in J. Soviet Math. Vol. 30, No. 4 (1985), 2287-2292.
    • (1983) Zapiski Nauchn. Sem. L O M I AN S S S R , vol.131 , pp. 72-79
    • IvocHKiNA, N. M.1
  • 35
    • 0002042456 scopus 로고
    • Solution of the Dirichlet problem for curvature equation of order m
    • Russian. English translation in Math.USSR-Sb., 67 2 (1990), 317-339
    • N. M. IvocHKiNA, Solution of the Dirichlet problem for curvature equation of order m. Math. Sbomik, Vol. 180 No. 7 (1989), 867-887 in Russian. English translation in Math.USSR-Sb., Vol. 67, No. 2 (1990), 317-339.
    • (1989) Math. Sbomik , vol.180 , Issue.7 , pp. 867-887
    • IvocHKiNA, N. M.1
  • 36
    • 0000362188 scopus 로고
    • The Dirichlet problem for the equations of curvature of order m
    • N. M. IvocHKiNA, The Dirichlet problem for the equations of curvature of order m, English translation in Leningrad Math. J. Vol. 2 No. 3 (1991), 631-654.
    • (1991) English translation in Leningrad Math. J , vol.2 , Issue.3 , pp. 631-654
    • IvocHKiNA, N. M.1
  • 37
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions offully nonlinear second order partial differential equations
    • B. JENSEN, The maximum principle for viscosity solutions offully nonlinear second order partial differential equations. Arch. Rational Mach. Anal. Vol. 101 No. 1 (1988), 1-27.
    • (1988) Arch. Rational Mach. Anal , vol.101 , Issue.1 , pp. 1-27
    • JENSEN, B.1
  • 38
    • 84981758023 scopus 로고
    • Degenerate elliptic-parabolic equations of second order
    • HN ?ni
    • J. J. KoHN - L. NIRENBERG, Degenerate elliptic-parabolic equations of second order. Comm. Pure and Appl. Math. Vol. 20, No. 4 (1967), 191-?ni.
    • (1967) Comm. Pure and Appl. Math , vol.20 , Issue.4 , pp. 191
    • Ko, J. J.1    NIRENBERG, L.2
  • 39
    • 84990625867 scopus 로고
    • A priori interior gradient bounds for solutions to elliptic Weingarten equations
    • N. J. KOREVAAR, A priori interior gradient bounds for solutions to elliptic Weingarten equations, Ann. Inst. Henri Poincaré, Analyse non lineaire, Vol. 4 No. 5 (1987), 405-421.
    • (1987) Ann. Inst. Henri Poincaré, Analyse non lineaire , vol.4 , Issue.5 , pp. 405-421
    • KOREVAAR, N. J.1
  • 40
    • 0000396066 scopus 로고
    • Boundedly nonhomogeneous elliptic and parabolic equations
    • English translation in Math. USSR Izvestija, 2 3 (1983), 459-492
    • N. V. KRYLOV, Boundedly nonhomogeneous elliptic and parabolic equations, Izvestija Akad. Nauk SSSR, ser. mat. Vol. 46 No. 3 (1982), 487-523. English translation in Math. USSR Izvestija, Vol. 20 No. 3 ( 1983), 459-492.
    • (1982) Izvestija Akad. Nauk SSSR, ser. mat , vol.46 , Issue.3 , pp. 487-523
    • KRYLOV, N. V.1
  • 41
    • 0002296910 scopus 로고
    • Boundedly nonhomogeneous elliptic and parabolic equations in a domain
    • English translation in Math. USSR Izvestija 2 1 (1984), 67-97
    • N. V. KRYLOV, Boundedly nonhomogeneous elliptic and parabolic equations in a domain, Izvestija Akad. Nauk SSSR, ser. mat., Vol. 47 No. 1 (1983), 75-108. English translation in Math. USSR Izvestija Vol. 22 No. 1 (1984), 67-97.
    • (1983) Izvestija Akad. Nauk SSSR, ser. mat , vol.47 , Issue.1 , pp. 75-108
    • KRYLOV, N. V.1
  • 42
    • 77951444062 scopus 로고
    • On degenerate nonlinear elliptic equations II
    • Russian. English translation in Math. USSR Sbornik 4 1 (1984), 207-228
    • N. V. KRYLOV, On degenerate nonlinear elliptic equations II, Matematicheski Sbornik, Vol. 121 No. 2 (1983), 211-232 in Russian. English translation in Math. USSR Sbornik Vol. 49 No. 1 (1984), 207-228.
    • (1983) Matematicheski Sbornik , vol.121 , Issue.2 , pp. 211-232
    • KRYLOV, N. V.1
  • 43
    • 0039985200 scopus 로고
    • On estimates for the derivatives of solutions of nonlinear parabolic equations
    • English translation in Soviet Math. Dokl. 2 1 (1984), 14-17
    • N. V. KRYLOV, On estimates for the derivatives of solutions of nonlinear parabolic equations, Doklady Acad. Nauk SSSR, Vol. 274 No. 1 (1984), 23-26. English translation in Soviet Math. Dokl. Vol. 29 No. 1 (1984), 14-17.
    • (1984) Doklady Acad. Nauk SSSR , vol.274 , Issue.1 , pp. 23-26
    • KRYLOV, N. V.1
  • 45
    • 84972517793 scopus 로고
    • Some new results in the theory of nonlinear elliptic and parabolic equations
    • N. V. KRYLOV, Some new results in the theory of nonlinear elliptic and parabolic equations, Proceed. of Intern. Congr. of Math., Berkeley Vol. 2 (1986), 1101-1109.
    • (1986) Proceed. of Intern. Congr. of Math., Berkeley , vol.2 , pp. 1101-1109
    • KRYLOV, N. V.1
  • 46
    • 85129392503 scopus 로고    scopus 로고
    • Smoothness of the value function for a controlled diffusion process in a domain
    • 3 N o. 1 (1 9 8 9), 6 6 9 6 i n Russian. English translation i n Math. USSR I z e s t i j a 3 4, N o. 1 (1 9 9 0), 6 5 9 6
    • N. V. KRYLOV, Smoothness of the value function for a controlled diffusion process in a domain, Izvestija Akad. Nauk SSSR, ser. mat. Vol. 5 3 N o. 1 (1 9 8 9), 6 6 - 9 6 i n Russian. English translation i n Math. USSR I z v e s t i j a Vol. 3 4, N o. 1 (1 9 9 0), 6 5 - 9 6 .
    • Izvestija Akad. Nauk SSSR, ser. mat , vol.5
    • KRYLOV, N. V.1
  • 47
    • 85129406815 scopus 로고
    • On first quasiderivatives of solutions of Ito's stochastic equations
    • 3 9 8 4 2 6 i n Russian. English translation i n Math. USSR I z e s t i j a 4 0
    • N. V. KRYLOV, On first quasiderivatives of solutions of Ito's stochastic equations, Izvestija Akad. Nauk SSSR, ser. mat. Vol. 5 6 N o. 2 (1 9 9 2), 3 9 8 - 4 2 6 i n Russian. English translation i n Math. USSR I z v e s t i j a Vol. 4 0 (1993).
    • (1993) Izvestija Akad. Nauk SSSR, ser. mat. Vol. 5 6 N o. 2 (1 9 9 2)
    • KRYLOV, N. V.1
  • 49
    • 84963254755 scopus 로고
    • Interior first order derivative estimates for solutions of nonlinear degenerate elliptic equations with constant coefficients
    • N o
    • N. V. KRYLOV, Interior first order derivative estimates for solutions of nonlinear degenerate elliptic equations with constant coefficients. C o m m. in P D E, Vol. 18 N o. 1-2 (1993), 1-40.
    • (1993) C o m m. in P D E , vol.18 , Issue.1-2 , pp. 1-40
    • KRYLOV, N. V.1
  • 50
    • 3342976738 scopus 로고    scopus 로고
    • On the general notion of fully nonlinear second order elliptic equation
    • 4 7 N o. 3, (1 9 9 5)
    • N. V. KRYLOV, On the general notion of fully nonlinear second order elliptic equation. Trans. Amer. Math. S o c. Vol. 3 4 7 N o. 3, (1 9 9 5), 8 5 7 - 8 9 5.
    • Trans. Amer. Math. S o c , vol.3 , pp. 857-895
    • KRYLOV, N. V.1
  • 51
    • 0038872566 scopus 로고    scopus 로고
    • A theorem on degenerate elliptic Bellman equations in bounded domains
    • N o. (1 9 9 5)
    • N. V. KRYLOV, A theorem on degenerate elliptic Bellman equations in bounded domains. Differential a n d Integr. E q. Vol. 8 N o. 5 (1 9 9 5), 9 6 1 - 9 8 0.
    • Differential a n d Integr. E q , vol.8 , Issue.5 , pp. 961-980
    • KRYLOV, N. V.1
  • 52
    • 0041132744 scopus 로고    scopus 로고
    • An estimate of the probability that a diffusion process hits a set of positive measure, D o k l a d y A c a d
    • 5 N o. 1 (1 9 7 9), English translation i n S o i e t Math. D o k l. 2 0 N o. 2 (1 9 7 9), 2 5 3 2 5 5
    • N. V. KRYLOV - M. V. SKVÖHOW, An estimate of the probability that a diffusion process hits a set of positive measure, D o k l a d y A c a d. Nauk SSSR Vol. 2 4 5 N o. 1 (1 9 7 9), 1 8 - 2 0. English translation i n S o v i e t Math. D o k l. Vol. 2 0 N o. 2 (1 9 7 9), 2 5 3 - 2 5 5 .
    • Nauk SSSR , vol.2 4 , pp. 18-20
    • KRYLOV, N. V.1    SKVÖHOW, M. V.2
  • 53
    • 0009321268 scopus 로고
    • A certain property of solutions of parabolic equations with measurable coefficients
    • M. S A F O N O Vol. 4 N o. 1 1 6 1 1 7 5. English translation i n Math. USSR I z e s t i j a, 16, N o. 1 (1 9 8 1), 1 5 1 1 6 4
    • N. V. KRYLOV - M. V. S A F O N O V, A certain property of solutions of parabolic equations with measurable coefficients, Izvestija Akad. Nauk SSSR, ser. m a t. Vol. 4 4 N o. 1 (1980), 1 6 1 - 1 7 5. English translation i n Math. USSR I z v e s t i j a, Vol. 16, N o. 1 (1 9 8 1), 1 5 1 - 1 6 4.
    • (1980) Izvestija Akad. Nauk SSSR, ser. m a t , vol.4
    • KRYLOV, N. V.1
  • 54
    • 0026821779 scopus 로고    scopus 로고
    • Discrete methods for fully nonlinear elliptic equations
    • H. J. K u o (1 9 9 2)
    • H. J. K u o - N. S. TRUDINGER, Discrete methods for fully nonlinear elliptic equations, SIAM J. o n N u m e r. Anal. Vol. 2 9 (1 9 9 2), 1 2 3 - 1 3 5.
    • SIAM J. o n N u m e r. Anal , vol.2 9 , pp. 123-135
    • TRUDINGER, N. S.1
  • 55
    • 0040457644 scopus 로고
    • On the discrete maximum principleforparabolicdifference operators
    • H. J. K u o
    • H. J. K u o - N. S. liRiJYyiiGER, On the discrete maximum principleforparabolicdifference operators. Math. Modelling and Numer. Anal. Vol. 27 No. 6 (1993), 719-737.
    • (1993) Math. Modelling and Numer. Anal , vol.27 , Issue.6 , pp. 719-737
    • liRiJYyiiGER, N. S.1
  • 57
    • 51649147985 scopus 로고    scopus 로고
    • On the solvability of Mange-Ampère type equations in non-uniformly convex domains
    • 0 8 (1 9 9 1)
    • N. K u T E V, On the solvability of Mange-Ampère type equations in non-uniformly convex domains. Math. Z. Vol. 2 0 8 (1 9 9 1), 1 6 7 - 1 7 6.
    • Math. Z , vol.2 , pp. 167-176
    • K u T E V, N.1
  • 58
    • 84972512490 scopus 로고    scopus 로고
    • On the solvability of Dirichlet's problem for a class of nonlinear elliptic and parabolic equations
    • N. K u T E I n t e r n a t i o n a l Conference on Different i a l E q u a t i o n s, B a r s e l o n a, 2 6 3 1 A u g u s t 1 9 9 1, E d s: C. P e r e l l o, C. S i m ó and J. S o l a M o r a l e s, W o r l d S c i e n t i f i c
    • N. K u T E V, On the solvability of Dirichlet's problem for a class of nonlinear elliptic and parabolic equations, I n t e r n a t i o n a l Conference on Different i a l E q u a t i o n s, B a r s e l o n a, 2 6 - 3 1 A u g u s t 1 9 9 1, E d s: C. P e r e l l o, C. S i m ó and J. S o l a - M o r a l e s, W o r l d S c i e n t i f i c, S i n g a p o r e - N e w J e r s e y - L o n d o n - H o n g K o n g Vol. 2, 6 6 6 - 6 7 0.
    • S i n g a p o r e - N e w J e r s e y - L o n d o n - H o n g K o n g , vol.2 , pp. 666-670
  • 59
    • 33646467674 scopus 로고    scopus 로고
    • A priori limitations for solutions ofMonge-Ampère equations I, II
    • H. L E W Y, (1 9 3 5), 4 2 (1 9 3 7), 3 6 5 3 7 4
    • H. L E W Y, A priori limitations for solutions ofMonge-Ampère equations I, II, Trans. Amer. Math. S o c. Vol. 3 7 (1 9 3 5), 4 1 7 - 4 3 4; Vol. 4 2 (1 9 3 7), 3 6 5 - 3 7 4.
    • Trans. Amer. Math. S o c , vol.3 7 , pp. 417-434
  • 60
    • 84967800148 scopus 로고
    • Nonlinear oblique boundary value problems for nonlinear elliptic equations
    • G. M. L i B E R M A N 9 5 N o. 2
    • G. M. L i B E R M A N - N. S. TRUDmcER, Nonlinear oblique boundary value problems for nonlinear elliptic equations. Trans. Amer. Math. S o c. Vol. 2 9 5 N o. 2 (1986), 5 0 9 - 5 4 6 .
    • (1986) Trans. Amer. Math. S o c , vol.2 , pp. 509-546
    • TRUDmcER, N. S.1
  • 62
    • 0002043438 scopus 로고
    • Viscosity solutions offully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part III Uniqueness of viscosity solutions of general second order equations
    • P. L. LIONS, Viscosity solutions offully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part III Uniqueness of viscosity solutions of general second order equations, J. Funct. Anal. Vol. 86 (1989), 1-18.
    • (1989) J. Funct. Anal , vol.86 , pp. 1-18
    • LIONS, P. L.1
  • 63
    • 84967790541 scopus 로고
    • Neumann problems for uniformly elliptic Bellman equations
    • P. L. LIONS - N. S. TRUDINGER, Neumann problems for uniformly elliptic Bellman equations. Math. Z., Vol. 191 (1985), 1-15.
    • (1985) Math. Z , vol.191 , pp. 1-15
    • LIONS, P. L.1    TRUDINGER, N. S.2
  • 64
    • 84990557141 scopus 로고
    • The Neumann problem for equations ofMonge-Ampère type
    • P.L. LIONS - N.S. TRUDINGER - J.I.E. URBAS, The Neumann problem for equations ofMonge-Ampère type. Comm. Pure Appl. Math. Vol. 39 (1986), 539-563.
    • (1986) Comm. Pure Appl. Math , vol.39 , pp. 539-563
    • LIONS, P.L.1    TRUDINGER, N.S.2    URBAS, J.I.E.3
  • 65
    • 33748504072 scopus 로고
    • Volumen und Oberfläche
    • H. MINKOWSKI, Volumen und Oberfläche, Math. Ann. Vol. 57 (1903).
    • (1903) Math. Ann , vol.57
    • MINKOWSKI, H.1
  • 66
    • 0346621865 scopus 로고
    • SU un problema di Minkowski
    • C. MIRANDA, SU un problema di Minkowski, Rend. Sem. Mat. Roma Vol. 3 (1939) .
    • (1939) Rend. Sem. Mat. Roma , vol.3
    • MIRANDA, C.1
  • 67
    • 84980088567 scopus 로고
    • The Weyl and Minkowski problems in differential geometry in the large
    • L. NIRENBERG, The Weyl and Minkowski problems in differential geometry in the large. Comm. Pure Appl. Math. Vol. 6 (1953).
    • (1953) Comm. Pure Appl. Math , vol.6
    • NIRENBERG, L.1
  • 68
    • 0001956337 scopus 로고
    • Second Order Equations with Nonnegative Characteristic form
    • O. A. O L E I N I K E. R A D K E I C H, I N I T I, Moscow, 1971 in Russian. English translation: Amer. Math. S o c, Plenum Press, Providence R. L
    • O. A. O L E I N I K - E. V. R A D K E V I C H, "Second Order Equations with Nonnegative Characteristic form", Itogi Nauki, Mat. Analiz 1969, V I N I T I, Moscow, 1971 in Russian. English translation: Amer. Math. S o c, Plenum Press, Providence R. L, 1973.
    • (1973) Itogi Nauki, Mat. Analiz 1969
  • 69
    • 0011869528 scopus 로고
    • Regularity of convex surfaces with prescribed Gaussian curvature
    • Russian
    • A. V. PoGORELOV, Regularity of convex surfaces with prescribed Gaussian curvature, Matem. Sbomik Vol. 3 1, 1 (1952), 88-103 in Russian.
    • (1952) Matem. Sbomik , vol.3 1 , Issue.1 , pp. 88-103
    • PoGORELOV, A. V.1
  • 71
    • 85129428558 scopus 로고    scopus 로고
    • The Dirichlet problem for the n-dimensional analogue of the Monge-Ampère equation, D o k l. A k a d
    • A. P O G O R E L O Nauk SSSR 0 1 N o. 4 (1 9 7 1), 7 9 0 7 9 3 i n Russian. English translation i n S o i e t Math. D o k l. 1 2 (1 9 7 1)
    • A. V. P O G O R E L O V, The Dirichlet problem for the n-dimensional analogue of the Monge-Ampère equation, D o k l. A k a d. Nauk SSSR Vol. 2 0 1 N o. 4 (1 9 7 1), 7 9 0 - 7 9 3 i n Russian. English translation i n S o v i e t Math. D o k l. Vol. 1 2 (1 9 7 1), 1 7 2 7 - 1 7 3 1 .
    • , vol.2 , pp. 1727-1731
  • 72
    • 0004170227 scopus 로고
    • Nauka, Moscow, 1975 in Russian. English translation: J. Wiley, New York
    • A. V. POGORELOV, "The Minkowski Multidimensional Problem", Nauka, Moscow, 1975 in Russian. English translation: J. Wiley, New York, 1978.
    • (1978) The Minkowski Multidimensional Problem
    • POGORELOV, A. V.1
  • 73
    • 24944568821 scopus 로고
    • Uniqueness of the solution of the Bellman equation in the case of general controlled random processes
    • Russian. English translation in Lithuanian Math. J. 2 2 (1982), 160-168
    • G. PRAGARAUSKAS, Uniqueness of the solution of the Bellman equation in the case of general controlled random processes. Lit. Mat. Sbomik Vol. 22 No. 2 (1982), 137-156 in Russian. English translation in Lithuanian Math. J. Vol. 22 No. 2 (1982), 160-168.
    • (1982) Lit. Mat. Sbomik , vol.22 , Issue.2 , pp. 137-156
    • PRAGARAUSKAS, G.1
  • 75
    • 85129408654 scopus 로고
    • Hamack inequality for elliptic equations and the Holder property of their solutions
    • 1 in Russian. English translation in J. Soviet Math. 2 5 (1983), 851-863
    • M. V. SAFONOV, Hamack inequality for elliptic equations and the Holder property of their solutions. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (L O M I) Vol. 96 (1980), 111-2, 1 in Russian. English translation in J. Soviet Math. Vol. 21 No. 5 (1983), 851-863.
    • (1980) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (L O M I) , vol.96 , pp. 111-112
    • SAFONOV, M. V.1
  • 76
    • 85129363163 scopus 로고    scopus 로고
    • On the classical solution of Bellman's elliptic equations, D o k l. A k a d
    • M. S A F O N O Nauk SSSR, 7 8 N o. 4 (1 9 8 4), 8 1 0 8 1 3 i n Russian. English translation i n S o i e t Math. D o k l. 3 0 N o. 2 (1 9 8 4)
    • M. V. S A F O N O V, On the classical solution of Bellman's elliptic equations, D o k l. A k a d. Nauk SSSR, Vol. 2 7 8 N o. 4 (1 9 8 4), 8 1 0 - 8 1 3 i n Russian. English translation i n S o v i e t Math. D o k l. Vol. 3 0 N o. 2 (1 9 8 4), 4 8 2 - 4 8 5 .
    • , vol.2 , pp. 482-485
  • 78
    • 0013027639 scopus 로고
    • On the classical solution ofnonlinear elliptic equations ofsecond order, Izvestija Akad
    • Nauk S S S R, ser. mat in Russian. English translation in Math. USSR Izvestija 3 3 (1989), 597-612
    • M. V. SAFONOV, On the classical solution ofnonlinear elliptic equations ofsecond order, Izvestija Akad. Nauk S S S R, ser. mat. Vol. 137 No. 2 (1988), 184-201 in Russian. English translation in Math. USSR Izvestija Vol. 33 No. 3 (1989), 597-612.
    • (1988) , vol.137 , Issue.2 , pp. 184-201
    • SAFONOV, M. V.1
  • 79
    • 38249013207 scopus 로고    scopus 로고
    • Viscosity solutions for Hamilton-Jacobi equations with unbounded nonlinear terms
    • (9 9 2)
    • D. TATARU, Viscosity solutions for Hamilton-Jacobi equations with unbounded nonlinear terms, J. Math. Anal. Appl. Vol. 163 (1 9 9 2), 3 4 5 - 3 9 2.
    • J. Math. Anal. Appl , vol.163 , Issue.1 , pp. 345-392
    • TATARU, D.1
  • 80
    • 0026839411 scopus 로고    scopus 로고
    • Viscosity solutions for the dynamic programming equations
    • (1 9 9 2)
    • D. TATARU, Viscosity solutions for the dynamic programming equations. A p p l i e d M a t h, a n d O p t i m i z. Vol. 2 5 (1 9 9 2), 1 0 9 - 1 2 6.
    • A p p l i e d M a t h, a n d O p t i m i z , vol.2 5 , pp. 109-126
    • TATARU, D.1
  • 81
    • 84967707828 scopus 로고
    • Fully nonlinear, uniformly elliptic equations under natural structure conditions
    • N. S. TRUDINGER, Fully nonlinear, uniformly elliptic equations under natural structure conditions. Trans. Amer. Math. Soc. Vol. 278 No. 2 (1983), 751-769.
    • (1983) Trans. Amer. Math. Soc , vol.278 , Issue.2 , pp. 751-769
    • TRUDINGER, N. S.1
  • 82
    • 84976123867 scopus 로고
    • Holder gradient estimates for fully nonlinear elliptic equations
    • N. S. TRUDINGER, Holder gradient estimates for fully nonlinear elliptic equations, Proc. Roy. Soc. Edinburgh, Sect. A Vol. 108 (1988), 57-65.
    • (1988) Proc. Roy. Soc. Edinburgh, Sect. A , vol.108 , pp. 57-65
    • TRUDINGER, N. S.1
  • 83
    • 84974397186 scopus 로고    scopus 로고
    • On the twice differentiability of viscosity solutions of nonlinear elliptic equations
    • (1 9 8 9), AAl
    • N. S. TRUDINGER, On the twice differentiability of viscosity solutions of nonlinear elliptic equations. B u l l. A u s t r a l. Math. S o c. Vol. 3 9 (1 9 8 9), AAZ-AAl.
    • B u l l. A u s t r a l. Math. S o c , vol.3 9 , pp. AAZ
    • TRUDINGER, N. S.1
  • 84
    • 0006460991 scopus 로고    scopus 로고
    • The Dirichlet problem for the prescribed curvature equations
    • (1 9 9 0)
    • N. S. TRUDINGER, The Dirichlet problem for the prescribed curvature equations. A r c h. R a t. M e c h. Anal. Vol. I l l N o. 2 (1 9 9 0), 1 5 3 - 1 7 9.
    • A r c h. R a t. M e c h. Anal. Vol. I l l N o , vol.2 , pp. 153-179
    • TRUDINGER, N. S.1
  • 85
    • 51249176790 scopus 로고
    • A priori bounds and necessary conditions for solvability ofprescribed curvature equations
    • N. S. TRUDINGER, A priori bounds and necessary conditions for solvability ofprescribed curvature equations, Manuscripta Nath. Vol. 67 (1990), 99-112.
    • (1990) Manuscripta Nath , vol.67 , pp. 99-112
    • TRUDINGER, N. S.1
  • 86
    • 84971113467 scopus 로고    scopus 로고
    • The Dirichlet problem for the equation of prescribed Gauss curvature
    • (1 9 8 3)
    • N. S. TRUDINGER - J. I. E. URBAS, The Dirichlet problem for the equation of prescribed Gauss curvature. B u l l. A u s t. Math. S o c. Vol. 2 8 (1 9 8 3), 2 1 7 - 2 3 1 .
    • B u l l. A u s t. Math. S o c , vol.2 8 , pp. 217-231
    • TRUDINGER, N. S.1    URBAS, J. I. E.2
  • 87
    • 84974054589 scopus 로고    scopus 로고
    • On second derivatives estimates for equations of Monge-Ampère type
    • 0 (1 9 8 4)
    • N. S. TRUDINGER - J. I. E. URBAS, On second derivatives estimates for equations of Monge-Ampère type. B u l l. A u s t r a l. Math. S o c. Vol. 3 0 (1 9 8 4), 3 2 1 - 3 3 4.
    • B u l l. A u s t r a l. Math. S o c , vol.3 , pp. 321-334
    • TRUDINGER, N. S.1    URBAS, J. I. E.2
  • 88
    • 84990622731 scopus 로고
    • Deforming a hypersurface by its Gauss-Kroneker curvature
    • K. Tso, Deforming a hypersurface by its Gauss-Kroneker curvature. Comm. Pure and Appl. Math Vol. 38 (1985), 867-882.
    • (1985) Comm. Pure and Appl. Math , vol.38 , pp. 867-882
    • Tso, K.1
  • 90
    • 0040845216 scopus 로고
    • Global Holder estimates for equations of Monge-Ampère type
    • J. I. E
    • J. I. E. Global Holder estimates for equations of Monge-Ampère type, Imtni. Math. Vol. 91 (1988), 1-29.
    • (1988) Imtni. Math , vol.91 , pp. 1-29
  • 91
    • 0000795112 scopus 로고
    • Regularity of generalized solutions of Monge-Ampère equations
    • J. I. E. URBAS, Regularity of generalized solutions of Monge-Ampère equations. Math. Zeit. Vol. 197 (1988), 365-393.
    • (1988) Math. Zeit , vol.197 , pp. 365-393
    • URBAS, J. I. E.1
  • 92
    • 0001448662 scopus 로고    scopus 로고
    • On the existence ofnonclassical solutions for two classes of fully nonlinear elliptic equations, I n d i a n a U n i v
    • N o. 4 (1 9 9 0)
    • J. I. E. URBAS, On the existence ofnonclassical solutions for two classes of fully nonlinear elliptic equations, I n d i a n a U n i v. Math. J. Vol. 3 9 N o. 4 (1 9 9 0), 3 5 5 - 3 8 2.
    • Math. J , vol.3 9 , pp. 355-382
    • URBAS, J. I. E.1
  • 93
    • 51249178113 scopus 로고    scopus 로고
    • On the expansion of star shaped hypersurfaces by symmetric functions of their principal curvatures
    • 0 5 (1 9 9 0)
    • J. I. E. URBAS, On the expansion of star shaped hypersurfaces by symmetric functions of their principal curvatures. Math. Z e i t. Vol. 2 0 5 (1 9 9 0), 3 5 5 - 3 7 2.
    • Math. Z e i t , vol.2 , pp. 355-372
    • URBAS, J. I. E.1
  • 94
    • 84975992620 scopus 로고
    • Regularity ofalmost extremal solutions ofMonge-Ampère equations
    • J. I. E. URBAS, Regularity ofalmost extremal solutions ofMonge-Ampère equations, Proc. Royal Soc. Edinburgh A Vol. 117 (1991), 21-29.
    • (1991) Proc. Royal Soc. Edinburgh A , vol.117 , pp. 21-29
    • URBAS, J. I. E.1
  • 95
    • 85129378276 scopus 로고    scopus 로고
    • Boundary regularity for solutions of the equation of prescribed Gauss curvature, A n n. I n s t. H e n r i P o i n c a r é
    • N o. (1 9 9 1)
    • J. I. E. URBAS, Boundary regularity for solutions of the equation of prescribed Gauss curvature, A n n. I n s t. H e n r i P o i n c a r é, A n a l y s e n o n Hneaire Vol. 8 N o. 5 (1 9 9 1), 4 9 9 - 5 2 2 .
    • A n a l y s e n o n Hneaire , vol.8 , Issue.5 , pp. 499-522
    • URBAS, J. I. E.1
  • 96
    • 84972517049 scopus 로고
    • An expansion of convex hypersurfaces
    • corrections to, ibid. 35, 763-765
    • J. I. E. URBAS, An expansion of convex hypersurfaces, J. Diff. Geom. Vol. 33 (1991), 91-125; corrections to, ibid. Vol 35, 763-765.
    • (1991) J. Diff. Geom , vol.33 , pp. 91-125
    • URBAS, J. I. E.1
  • 98
    • 85129451372 scopus 로고    scopus 로고
    • On the regularity theory of fully nonlinear parabolic equations I-III
    • W A N G L I H E, (1 9 9 2), 1 7 8, 2 5 5 2 6 2
    • W A N G L I H E, On the regularity theory of fully nonlinear parabolic equations I-III, C o m m. P u r e Appl. Math. Vol. 4 5 (1 9 9 2), 2 7 - 7 6, 1 4 1 - 1 7 8, 2 5 5 - 2 6 2.
    • C o m m. P u r e Appl. Math , vol.4 5 , pp. 27-76141
  • 99
    • 0038888541 scopus 로고    scopus 로고
    • On existence, uniqueness and regularity of viscosity solutions for the first initial boundary value problems to parabolic Monge-Ampère equation
    • W A N G R O U H U A I W A N G G U A N G U E. N o. (1 9 9 2)
    • W A N G R O U H U A I - W A N G G U A N G U E. On existence, uniqueness and regularity of viscosity solutions for the first initial boundary value problems to parabolic Monge-Ampère equation. Northeastern Math. J. Vol. 8 N o. 4 (1 9 9 2), 4 1 7 - 4 4 6.
    • Northeastern Math. J , vol.8 , Issue.4 , pp. 417-446
  • 100
    • 0012150697 scopus 로고
    • The geometric measure theoretical characterization of viscosity solutions to parabolic Monge-Ampère type equation
    • W A N G R O U H U A I W A N G G U A N G U E. N o
    • W A N G R O U H U A I - W A N G G U A N G U E. The geometric measure theoretical characterization of viscosity solutions to parabolic Monge-Ampère type equation, J. P a r t i a l D i f f. E q s. Vol. 6 N o. 3 (1993), 2 3 7 - 2 5 4.
    • (1993) J. P a r t i a l D i f f. E q s , vol.6 , Issue.3 , pp. 237-254


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.