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.
Citation
Tusheng Zhang. "A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients." Ann. Probab. 39 (4) 1502 - 1527, July 2011. https://doi.org/10.1214/10-AOP591
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