A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients

Abstract

In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of Dirichlet processes and backward stochastic differential equations play a crucial role.

Published in at http://dx.doi.org/10.1214/10-AOP591 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Time-reversal and elliptic boundary value problems

Cited by in corpus (2)

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• Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups