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

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. "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

Information

Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1242.60072
MathSciNet: MR2857248
Digital Object Identifier: 10.1214/10-AOP591

Subjects:
Primary: 60H30
Secondary: 31C25 , 35J25

Keywords: Backward stochastic differential equations , Dirichlet boundary value problems , Dirichlet processes , Fukushima’s decomposition , martingale representation theorem , Quadratic forms , weak solutions

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • July 2011
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