A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations
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- by R. Jensen, P.-L. Lions and P. E. Souganidis
- Proc. Amer. Math. Soc. 102 (1988), 975-978
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934877-2
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Abstract:
In this note we extend some recent results of R. Jensen concerning the uniqueness of viscosity solutions of scalar, second order, fully nonlinear, elliptic, possibly degenerate, partial differential equations.References
- A. D. Alexandrov, Majorization of solutions of second-order linear equations, Amer. Math. Soc. Transl. 68 (1968), 120-143.
- Jean-Michel Bony, Principe du maximum dans les espaces de Sobolev, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A333–A336 (French). MR 223711
- Michael G. Crandall, Hitoshi Ishii, and Pierre-Louis Lions, Uniqueness of viscosity solutions of Hamilton-Jacobi equations revisited, J. Math. Soc. Japan 39 (1987), no. 4, 581–596. MR 905626, DOI 10.2969/jmsj/03940581
- Michael G. Crandall and Pierre-Louis Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), no. 1, 1–42. MR 690039, DOI 10.1090/S0002-9947-1983-0690039-8
- Wendell H. Fleming and Raymond W. Rishel, Deterministic and stochastic optimal control, Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975. MR 0454768
- W. H. Fleming and P. E. Souganidis, Two-player, zero-sum stochastic differential games, Analyse mathématique et applications, Gauthier-Villars, Montrouge, 1988, pp. 151–164. MR 956957
- Robert Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Rational Mech. Anal. 101 (1988), no. 1, 1–27. MR 920674, DOI 10.1007/BF00281780
- Robert Jensen and Pierre-Louis Lions, Some asymptotic problems in fully nonlinear elliptic equations and stochastic control, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), no. 1, 129–176. MR 752583
- J.-M. Lasry and P.-L. Lions, A remark on regularization in Hilbert spaces, Israel J. Math. 55 (1986), no. 3, 257–266. MR 876394, DOI 10.1007/BF02765025
- P.-L. Lions, Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. I. The dynamic programming principle and applications, Comm. Partial Differential Equations 8 (1983), no. 10, 1101–1174. MR 709164, DOI 10.1080/03605308308820297
- P.-L. Lions, Fully nonlinear elliptic equations and applications, Nonlinear analysis, function spaces and applications, Vol. 2 (Písek, 1982) Teubner-Texte zur Mathematik, vol. 49, Teubner, Leipzig, 1982, pp. 126–149. MR 684999
- P.-L. Lions, A remark on Bony maximum principle, Proc. Amer. Math. Soc. 88 (1983), no. 3, 503–508. MR 699422, DOI 10.1090/S0002-9939-1983-0699422-3
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 975-978
- MSC: Primary 35B25; Secondary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934877-2
- MathSciNet review: 934877