Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients
Probability
2011-12-15 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.1112.3148,
title = {Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients},
author = {Xue Yang and Tusheng Zhang},
journal= {arXiv preprint arXiv:1112.3148},
year = {2011}
}