A probabilistic approach to Dirichlet problems of semilinear elliptic   PDEs with singular coefficients
  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. 
Tusheng Zhang
math.PR