A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients
Probability
2012-11-19 v1
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.
Keywords
Cite
@article{arxiv.1211.3820,
title = {A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients},
author = {Tusheng Zhang},
journal= {arXiv preprint arXiv:1211.3820},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AOP591 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)