Time-reversal and elliptic boundary value problems

Zhen Qing Chen; Tusheng Zhang

doi:10.1214/08-AOP427

Time-reversal and elliptic boundary value problems

Zhen Qing Chen, Tusheng Zhang

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

18 Citations (Scopus)

Abstract

In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.

Original language	English
Pages (from-to)	1008-1043
Number of pages	36
Journal	Annals of Probability
Volume	37
Issue number	3
DOIs	https://doi.org/10.1214/08-AOP427
Publication status	Published - May 2009
Externally published	Yes

Keywords

Boundary value problem
Diffusion
Feynman-kac transform
Girsanov transform
Multiplicative functional
Partial differential equation
Probabilistic representation
Quadratic form
Time-reversal
Weak solution

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10.1214/08-AOP427

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abstract = "In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.",

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AB - In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.

KW - Boundary value problem

KW - Diffusion

KW - Feynman-kac transform

KW - Girsanov transform

KW - Multiplicative functional

KW - Partial differential equation

KW - Probabilistic representation

KW - Quadratic form

KW - Time-reversal

KW - Weak solution

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JO - Annals of Probability

JF - Annals of Probability

IS - 3

ER -

Time-reversal and elliptic boundary value problems

Abstract

Keywords

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