Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with   Singular Coefficients
  In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is probabilistic. The theory of Dirichlet forms and backward stochastic differential equations with singular coefficients and infinite horizon plays a crucial role. 
Xue Yang and Tusheng Zhang
math.PR math.AP