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Volumn 8, Issue 2, 2002, Pages 331-359

Topics in regularity and qualitative properties of solutions of nonlinear elliptic equations

Author keywords

A priori estimates; Fully nonlinear equations; Maximum principles; Nonlinear elliptic PDE; Symmetry properties

Indexed keywords


EID: 23044534434     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2002.8.331     Document Type: Article
Times cited : (35)

References (25)
  • 1
    • 0003158115 scopus 로고
    • Certain estimates for the Dirichlet problem
    • A. D. Alexandroff, Certain estimates for the Dirichlet problem. Soviet. Math. Dokl. 1 (1960), 1151-1154.
    • (1960) Soviet. Math. Dokl. , vol.1 , pp. 1151-1154
    • Alexandroff, A.D.1
  • 2
    • 0039993142 scopus 로고
    • Uniqueness conditions and estimates for the solution of the Dirichlet problem
    • A. D. Alexandroff, Uniqueness conditions and estimates for the solution of the Dirichlet problem. Amer. Math. Soc. Transl. 68 (1968), 89-119.
    • (1968) Amer. Math. Soc. Transl. , vol.68 , pp. 89-119
    • Alexandroff, A.D.1
  • 3
    • 0000054308 scopus 로고
    • Theory of quasilinear equations
    • I. Ya Bakelman, Theory of quasilinear equations. (Russian) Sibirsk. Mat. Ž. 2 (1961), 179-186.
    • (1961) Sibirsk. Mat. Ž , vol.2 , pp. 179-186
    • Bakelman, I.Ya.1
  • 5
    • 0001440517 scopus 로고    scopus 로고
    • Inequalities for second-order elliptic equations with applications to unbounded domains I
    • H. Berestycki, L. A. Caffarelli, L. Nirenberg, Inequalities for second-order elliptic equations with applications to unbounded domains I. Duke Math. J. 81 (1996), 467-194.
    • (1996) Duke Math. J. , vol.81 , pp. 467-1194
    • Berestycki, H.1    Caffarelli, L.A.2    Nirenberg, L.3
  • 6
    • 0000840471 scopus 로고
    • Some qualitative properties of semilinear elliptic equations in a cylinder
    • ed. P. Rabinowitz et al., Academic Press, Boston
    • H. Berestycki, L. Nirenberg, Some qualitative properties of semilinear elliptic equations in a cylinder, Analysis Et Cetera, ed. P. Rabinowitz et al., Academic Press, Boston, 1990, pp. 115-164.
    • (1990) Analysis et Cetera , pp. 115-164
    • Berestycki, H.1    Nirenberg, L.2
  • 8
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second order elliptic operators in general domains
    • H. Berestycki, L. Nirenberg, S. R. S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operators in general domains. Comm. Pure Appl. Math. 47 (1994), 47-92.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 9
    • 84990710937 scopus 로고
    • On the Alexandraff-Bakelman-Pucci estimate and the reversed Holder inequality for solutions of elliptic and parabolic equations
    • X. Cabré, On the Alexandraff-Bakelman-Pucci estimate and the reversed Holder inequality for solutions of elliptic and parabolic equations. Comm. Pure Appl. Math. 48 (1995), 539-570.
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 539-570
    • Cabré, X.1
  • 11
    • 0000898166 scopus 로고
    • Interior a priori estimates for solutions of fully nonlinear equations
    • L. A. Caffarelli, Interior a priori estimates for solutions of fully nonlinear equations. Ann. of Math. 130 (1989), 89-213.
    • (1989) Ann. of Math. , vol.130 , pp. 89-213
    • Caffarelli, L.A.1
  • 12
    • 0002449458 scopus 로고
    • Fully nonlinear elliptic equations
    • American Math. Society
    • L. A. Caffarelli, X. Cabré, Fully nonlinear elliptic equations. Colloquium Publications 43, American Math. Society, 1995.
    • (1995) Colloquium Publications , vol.43
    • Caffarelli, L.A.1    Cabré, X.2
  • 13
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M. G. Crandall, P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983), 1-42.
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.L.2
  • 14
    • 84990553687 scopus 로고
    • Classical solutions of fully nonlinear, convex, second-order elliptic equations
    • L. C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math. 25 (1982), 333-363.
    • (1982) Comm. Pure Appl. Math. , vol.25 , pp. 333-363
    • Evans, L.C.1
  • 16
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • B. Gidas, W.-M. Ni, L. Nirenberg, Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979), 209-243.
    • (1979) Comm. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.-M.2    Nirenberg, L.3
  • 18
    • 84990575194 scopus 로고
    • On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's
    • H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic PDE's. Comm. Pure Appl. Math. 42 (1989), 15-46.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 15-46
    • Ishii, H.1
  • 19
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
    • R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations. Arch. Rat. Mech. Anal. 101 (1988), 1-27.
    • (1988) Arch. Rat. Mech. Anal. , vol.101 , pp. 1-27
    • Jensen, R.1
  • 20
    • 84878313116 scopus 로고
    • Boundedly nonhomogeneous elliptic and parabolic equations
    • N. V. Krylov, Boundedly nonhomogeneous elliptic and parabolic equations. Math. USSR Izv. 20 (1983), 459-492.
    • (1983) Math. USSR Izv. , vol.20 , pp. 459-492
    • Krylov, N.V.1
  • 21
    • 0039753684 scopus 로고
    • Boundedly nonhomogeneous elliptic and parabolic equations in a domain
    • N. V. Krylov, Boundedly nonhomogeneous elliptic and parabolic equations in a domain. Math. USSR Izv. 22 (1984), 67-97.
    • (1984) Math. USSR Izv. , vol.22 , pp. 67-97
    • Krylov, N.V.1
  • 22
    • 0003703449 scopus 로고
    • Nonlinear elliptic and parabolic equations of the second order
    • Reidel
    • N. V. Krylov, Nonlinear elliptic and parabolic equations of the second order, Mathematics and its Applications, Reidel, 1987.
    • (1987) Mathematics and Its Applications
    • Krylov, N.V.1
  • 23
    • 0001624778 scopus 로고
    • An estimate of the probability that a diffusion process hits a set of positive measure
    • N. V. Krylov, M. V. Safonov, An estimate of the probability that a diffusion process hits a set of positive measure. Soviet Math. Dokl. 20 (1979), 253-255.
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 253-255
    • Krylov, N.V.1    Safonov, M.V.2
  • 24
    • 0009321268 scopus 로고
    • Certain properties of solutions of parabolic equations with measurable coefficients
    • N. V. Krylov, M. V. Safonov, Certain properties of solutions of parabolic equations with measurable coefficients, (Russian), Izvestia Akad. Nauk SSSR 44 (1980), 161-175.
    • (1980) Izvestia Akad. Nauk SSSR , vol.44 , pp. 161-175
    • Krylov, N.V.1    Safonov, M.V.2
  • 25
    • 0001796926 scopus 로고
    • Limitazioni di equazioni ellittiche
    • C. Pucci, Limitazioni di equazioni ellittiche. Ann. Mat. Pura. Appl. 74 (1966), 15-30.
    • (1966) Ann. Mat. Pura. Appl. , vol.74 , pp. 15-30
    • Pucci, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.