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Volumn 29, Issue 5, 1998, Pages 1067-1086

Hopf-type estimates and formulas for nonconvex nonconcave Hamilton-Jacobi equations

Author keywords

Hamilton Jacobi equations; Hopf's representation formulas; Lax Oleinik formula; Nonconvex Hamiltonians; Viscosity solutions

Indexed keywords


EID: 0032337389     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141096309629     Document Type: Article
Times cited : (12)

References (35)
  • 3
    • 0001324581 scopus 로고
    • On Hopf's formulas for solutions of Hamilton-Jacobi equations
    • M. BARDI AND L. C. EVANS, On Hopf's formulas for solutions of Hamilton-Jacobi equations, Nonlinear Anal., 8 (1984), pp. 1373-1381.
    • (1984) Nonlinear Anal. , vol.8 , pp. 1373-1381
    • Bardi, M.1    Evans, L.C.2
  • 4
    • 0000816594 scopus 로고
    • The non-convex multidimensional Riemann problem for Hamilton-Jacobi equations
    • M. BARDI AND S. OSHER, The non-convex multidimensional Riemann problem for Hamilton-Jacobi equations, Siam J. Math. Anal., 22 (1991), pp. 344-351.
    • (1991) Siam J. Math. Anal. , vol.22 , pp. 344-351
    • Bardi, M.1    Osher, S.2
  • 6
    • 0000378860 scopus 로고
    • Asymptotic behaviour of viscosity solutions of first order Hamilton-Jacobi equations
    • G. BARLES, Asymptotic behaviour of viscosity solutions of first order Hamilton-Jacobi equations, Ricerche Mat., 34 (1985), pp. 227-260.
    • (1985) Ricerche Mat. , vol.34 , pp. 227-260
    • Barles, G.1
  • 7
    • 38249033847 scopus 로고
    • Uniqueness for first-order Hamilton-Jacobi equations and Hopf formula
    • G. BARLES, Uniqueness for first-order Hamilton-Jacobi equations and Hopf formula, J. Differential Equations, 69 (1987), pp. 346-367.
    • (1987) J. Differential Equations , vol.69 , pp. 346-367
    • Barles, G.1
  • 11
    • 38249001625 scopus 로고
    • On viscosity and geometrical solutions of Hamilton-Jacobi equations
    • F. CARDIN, On viscosity and geometrical solutions of Hamilton-Jacobi equations, Nonlinear Anal., 20 (1993), pp. 713-719.
    • (1993) Nonlinear Anal. , vol.20 , pp. 713-719
    • Cardin, F.1
  • 12
    • 84968507121 scopus 로고
    • Some properties of viscosity solutions of Hamilton-Jacobi equations
    • M. CRANDALL, L. C. EVANS, AND P. L. LIONS, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 282 (1984), pp. 487-502.
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 487-502
    • Crandall, M.1    Evans, L.C.2    Lions, P.L.3
  • 13
    • 0040769563 scopus 로고
    • Hamilton's theory aid generalized solutions of the Hamilton-Jacobi equation
    • E. D. CONWAY AND E. HOPF, Hamilton's theory aid generalized solutions of the Hamilton-Jacobi equation, J. Math. Mech., 13 (1964), pp. 939-986.
    • (1964) J. Math. Mech. , vol.13 , pp. 939-986
    • Conway, E.D.1    Hopf, E.2
  • 14
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations
    • M. G. CRANDALL AND P. L. LIONS, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), pp. 1-42.
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 1-42
    • Crandall, M.G.1    Lions, P.L.2
  • 15
    • 0022693379 scopus 로고
    • On existence and uniqueness of solutions of Hamilton-Jacobi equations
    • M. G. CRANDALL AND P. L. LIONS, On existence and uniqueness of solutions of Hamilton-Jacobi equations, Nonlinear Anal., 10 (1986), pp. 353-370.
    • (1986) Nonlinear Anal. , vol.10 , pp. 353-370
    • Crandall, M.G.1    Lions, P.L.2
  • 16
    • 84968511145 scopus 로고
    • Numerical schemes for conservation laws via Hamilton-Jacobi equations
    • L. CORRIAS, M. FALCONE, AND R. NATALINI, Numerical schemes for conservation laws via Hamilton-Jacobi equations, Math. Comp., 64 (1995), pp. 555-580.
    • (1995) Math. Comp. , vol.64 , pp. 555-580
    • Corrias, L.1    Falcone, M.2    Natalini, R.3
  • 17
    • 0000759411 scopus 로고    scopus 로고
    • Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equation and conservation laws
    • L. CORRIAS, Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equation and conservation laws, SIAM J. Numer. Anal., 33 (1996), pp. 1534-1558.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1534-1558
    • Corrias, L.1
  • 19
    • 0000102847 scopus 로고
    • Some min-max methods for the Hamilton-Jacobi equation
    • L. C. EVANS, Some min-max methods for the Hamilton-Jacobi equation, Indiana Univ. Math. J., 33 (1984), pp. 31-50.
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 31-50
    • Evans, L.C.1
  • 20
    • 0000102846 scopus 로고
    • Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations
    • L. C. EVANS AND P. SOUGANIDIS, Differential games and representation formulas for solutions of Hamilton-Jacobi-Isaacs equations, Indiana Univ. Math. J., 33 (1984), pp. 773-797.
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 773-797
    • Evans, L.C.1    Souganidis, P.2
  • 22
    • 0000073921 scopus 로고
    • Generalized solutions of non-linear equations of first order
    • E. HOPF, Generalized solutions of non-linear equations of first order, J. Math. Mech., 14 (1965), pp. 951-973.
    • (1965) J. Math. Mech. , vol.14 , pp. 951-973
    • Hopf, E.1
  • 23
    • 0000102848 scopus 로고
    • Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations
    • H. ISHII, Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations, Indiana Univ. Math. J., 33 (1984), pp. 721-748.
    • (1984) Indiana Univ. Math. J. , vol.33 , pp. 721-748
    • Ishii, H.1
  • 24
    • 84972566521 scopus 로고
    • Perron's method for Hamilton-Jacobi equations
    • H. ISHII, Perron's method for Hamilton-Jacobi equations, Duke Math. J., 55 (1987), pp. 369-384.
    • (1987) Duke Math. J. , vol.55 , pp. 369-384
    • Ishii, H.1
  • 25
    • 0010962499 scopus 로고
    • Representation of solutions of Hamilton-Jacobi equations
    • H. ISHII, Representation of solutions of Hamilton-Jacobi equations, Nonlinear Anal., 12 (1988), pp. 121-146.
    • (1988) Nonlinear Anal. , vol.12 , pp. 121-146
    • Ishii, H.1
  • 26
    • 0013520874 scopus 로고
    • The Cauchy problem in the large for certain non-linear first order equations
    • S. N. KRUŽKOV, The Cauchy problem in the large for certain non-linear first order equations, Soviet Math. Dokl., 1 (1960), pp. 474-477.
    • (1960) Soviet Math. Dokl. , vol.1 , pp. 474-477
    • Kružkov, S.N.1
  • 27
    • 0037567813 scopus 로고
    • Generalized solutions of nonlinear first order equations with several independent variables, II
    • S. N. KRUŽKOV, Generalized solutions of nonlinear first order equations with several independent variables, II, Math. USSR-Sb., 1 (1967), pp. 93-116.
    • (1967) Math. USSR-Sb. , vol.1 , pp. 93-116
    • Kružkov, S.N.1
  • 28
    • 4243894620 scopus 로고
    • On the minmax representation of solutions of first order nonlinear equations
    • S. N. KRUŽKOV, On the minmax representation of solutions of first order nonlinear equations, Functional Anal. Appl., 2 (1969), pp. 128-136.
    • (1969) Functional Anal. Appl. , vol.2 , pp. 128-136
    • Kružkov, S.N.1
  • 29
    • 25044442981 scopus 로고
    • First order nonlinear equations and the differential games connected with them
    • in Russian
    • S. N. KRUŽKOV, First order nonlinear equations and the differential games connected with them, Uspekhi Mat. Nauk, 24 (1969), pp. 227-228 (in Russian).
    • (1969) Uspekhi Mat. Nauk , vol.24 , pp. 227-228
    • Kružkov, S.N.1
  • 31
    • 84968501412 scopus 로고
    • Hopf's formula and multi-time Hamilton-Jacobi equations
    • P. L. LIONS AND J. C. ROCHET, Hopf's formula and multi-time Hamilton-Jacobi equations, Proc. Amer. Math. Soc., 96 (1986), pp. 79-84.
    • (1986) Proc. Amer. Math. Soc. , vol.96 , pp. 79-84
    • Lions, P.L.1    Rochet, J.C.2
  • 32
    • 0000064129 scopus 로고
    • The Riemann problem for nonconvex scalar conservation laws and Hamilton-Jacobi equations
    • S. OSHER, The Riemann Problem for nonconvex scalar conservation laws and Hamilton-Jacobi equations, Proc. Amer. Math. Soc., 89 (1983), pp. 641-646.
    • (1983) Proc. Amer. Math. Soc. , vol.89 , pp. 641-646
    • Osher, S.1
  • 33
    • 0026204106 scopus 로고
    • High order essentially non-oscillatory schemes for Hamilton-Jacobi equations
    • S. OSHER AND C. W. SHU, High order essentially non-oscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., 28 (1991), pp. 907-922.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 907-922
    • Osher, S.1    Shu, C.W.2
  • 35
    • 85033891603 scopus 로고
    • On the representation of Lipschitz global solutions of the Cauchy problem for Hamilton-Jacobi equations
    • Ho Chi Minh City, Ho Chi Minh City Math. Soc.
    • T. D. VAN, M. D. THAN, AND M. HOANG, On the representation of Lipschitz global solutions of the Cauchy problem for Hamilton-Jacobi equations, in Proc. Internat. Conference Analysis and Mechanics of Continuous Media (Ho Chi Minh City), Ho Chi Minh City Math. Soc., 3 (1995), pp. 428-436.
    • (1995) Proc. Internat. Conference Analysis and Mechanics of Continuous Media , vol.3 , pp. 428-436
    • Van, T.D.1    Than, M.D.2    Hoang, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.