A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients

Tusheng Zhang

doi:10.1214/10-aop591

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arXiv · 1211.3820

A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients

Tusheng Zhang

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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.

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Tusheng Zhang. 2012-11-16. A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients. https://doi.org/10.1214/10-aop591

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