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May 2009 Time-reversal and elliptic boundary value problems
Zhen-Qing Chen, Tusheng Zhang
Ann. Probab. 37(3): 1008-1043 (May 2009). DOI: 10.1214/08-AOP427

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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Zhen-Qing Chen. Tusheng Zhang. "Time-reversal and elliptic boundary value problems." Ann. Probab. 37 (3) 1008 - 1043, May 2009. https://doi.org/10.1214/08-AOP427

Information

Published: May 2009
First available in Project Euclid: 19 June 2009

zbMATH: 1187.60064
MathSciNet: MR2537548
Digital Object Identifier: 10.1214/08-AOP427

Subjects:
Primary: 60J57, 60J70
Secondary: 31C25i, 35R05, 60G46, 60H05

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 3 • May 2009
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