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.Comment: 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