A probabilistic approach to dirichlet problems of semilinear elliptic pdes with singular coefficients

Tusheng Zhang

doi:10.1214/10-AOP591

A probabilistic approach to dirichlet problems of semilinear elliptic pdes with singular coefficients

Research output: Contribution to journal › Article › peer-review

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. © 2011 Institute of Mathematical Statistics.

Original language	English
Pages (from-to)	1502-1527
Number of pages	25
Journal	Annals of Probability
Volume	39
Issue number	4
DOIs	https://doi.org/10.1214/10-AOP591
Publication status	Published - Jul 2011

Keywords

Backward stochastic differential equations
Dirichlet boundary value problems
Dirichlet processes
Fukushima's decomposition
Martingale representation theorem
Quadratic forms
Weak solutions

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title = "A probabilistic approach to dirichlet problems of semilinear elliptic pdes with singular coefficients",

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. {\textcopyright} 2011 Institute of Mathematical Statistics.",

keywords = "Backward stochastic differential equations, Dirichlet boundary value problems, Dirichlet processes, Fukushima's decomposition, Martingale representation theorem, Quadratic forms, Weak solutions",

author = "Tusheng Zhang",

year = "2011",

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AU - Zhang, Tusheng

PY - 2011/7

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AB - 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. © 2011 Institute of Mathematical Statistics.

KW - Backward stochastic differential equations

KW - Dirichlet boundary value problems

KW - Dirichlet processes

KW - Fukushima's decomposition

KW - Martingale representation theorem

KW - Quadratic forms

KW - Weak solutions

U2 - 10.1214/10-AOP591

DO - 10.1214/10-AOP591

M3 - Article

VL - 39

SP - 1502

EP - 1527

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

A probabilistic approach to dirichlet problems of semilinear elliptic pdes with singular coefficients

Abstract

Keywords

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