The probabilistic solution of the Dirichlet problem for degenerate elliptic equations

• Autorzy: Liu, C. , Morimoto, H.
• Języki publikacji: EN

Abstrakty

EN

We study the Dirichlet problem for degenerate elliptic equations, and show that the probabilistic solution is a unique viscosity solution.

Słowa kluczowe

PL

stochastyczne równanie różniczkowe

EN

stochastic differential equations; viscosity solutions

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: Vol. 54, no 2
• Strony: 163-174
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Liu, C.

autor

Morimoto, H.

• Liu School of Mathematics and Statistics, Southwest University, ChongQing, 400715, China,

Bibliografia

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• [6} W. H. Fleming and H. M. Soner, Controlled Markov Processes and Viscosity Solutions, Springer, New York, 1993.
• [7] W. D. Gerhard, The probabilistic solution of the Dirichlet problem for ½∆+(a, [Nabla])+b with singular coefficients, 3. Theoret. Probab. 5 (1992), 503-520.
• [8] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, New York, 1983.
• [9] I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York, 1991.
• [10] S. Koike, A Beginner's Guide to the Theory of Viscosity Solutions, MSJ Memoirs, Math. Soc. Japan, 2004.
• [11] E. Pardoux, Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and ellipptic PDEs of second order, in: Stochastic Analysis and Related Topics VI, Birkhäuser, 1998, 79-127.
• [12] A. Rozkosz, Probabilistic solutions of quasilinear PDE's, Bull. Polish Acad. Sci. Math. 48 (2000), 103-111.