Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients

Details Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients Mixed Boundary Value Problems of Semilinear Elliptic PDEs and BSDEs with Singular Coefficients

2011-12-14

arxiv.org/abs/1112.3148v1

Mathematics

Probability

Scientific paper

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.

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