On Hopf's formula for Lipschitz solutions of the Cauchy problem for Hamilton-Jacobi equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 29, Issue 10, 1997, Pages 1145-1159

  Van, Tran Duc ^a   Hoang, Nguyen ^a   Tsuji, Mikio ^b  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

^b KYOTO SANGYO UNIVERSITY   (Japan)

Author keywords

Hamilton Jacobi equations; Hopf's formula; Lipschitz solutions; Multivalued functions

Indexed keywords

EQUATIONS OF MOTION; FUNCTIONS; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING;

HAMILTON JACOBI EQUATIONS; HOPF'S FORMULA; LIPSCHITZ CONTINUITY;

BOUNDARY VALUE PROBLEMS;

EID: 0031281723     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00085-5     Document Type: Article

References (13)

1. Hopf, E., Generalized solutions of nonlinear equations of first order. J. Math. Mech., 1965, 14, 951-973.
2. Crandall, M. G. and Lions, P. L., Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. math. Soc., 1983, 277, 1-42.
3. Crandall, M. G., Evans, L. C. and Lions, P. L., Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Am. math. Soc., 1984, 282, 487-502.
4. Crandall, M. G., Ishii, H. and Lions, P. L., User's guide to viscosity solutions of second-order partial differential equations. Bull. Am. math. Soc., 1992, 27, 1-67.
5. Bardi, M. and Evans, L. C., On Hopf's formulas for solutions of Hamilton-Jacobi equations. Nonlinear Analysis, 1984, 8, 1373-1381.
6. Tran Duc Van and Nguyen Duy Thai Son, On a class of Lipschitz continuous functions of several variables. Proc. Am. math. Soc., 1994, 121, 865-870.
7. Tran Duc Van and Nguyen Duy Thai Son, Uniqueness of global quasi-classical solutions of the Cauchy problem for first-order nonlinear partial differential equations (in Russian), Differentsialnye Uravneniya, 1994, 30, 712-719.
8. Tran Duc Van, Nguyen Hoang and Gorenflo, R., Existence of global quasi-classical solutions of the Cauchy problem for Hamilton-Jacobi equations (in Russian). Differentsialnye Uravneniya, 1995, 31, 672-676.
9. Subbotin, A. I., Minimax Inequalities and Hamilton-Jacobi Equations (in Russian). Nauka, Moscow, 1991.
10. Aubin, J. P. and Frankowska, H., Set-Valued Analysis. Birkhäuser, 1990.
11. Rockafellar, T., Convex Analysis. Princeton University Press, 1970.
12. Horst, R. and Tuy, H., Global Optimization. Springer-Verlag, 1990.
13. Alexandrov, A. D., On surfaces which may be represented by a difference of convex functions (in Russian). Dokl. Acad. Nauk. SSSR, 1950, 72, 613-616.