A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients-Reference-Cited by-同舟云学术

A probabilistic approach to mixed boundary value problems for elliptic operators with singular coefficients

Published:2014-03-13 Issue:6 Volume:142 Page:2135-2149
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chen Zhen-Qing,Zhang Tusheng

Abstract

In this paper, we establish existence and uniqueness of solutions of a class of mixed boundary value problems for elliptic operators with singular coefficients. Our approach is probabilistic. The theory of Dirichlet forms plays an important role.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2014-142-06/S0002-9939-2014-11907-1/S0002-9939-2014-11907-1.pdf

Reference28 articles.

1. First eigenvalues and comparison of Green’s functions for elliptic operators on manifolds or domains;Ancona, Alano;J. Anal. Math.,1997

2. Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains;Bass, Richard F.;Ann. Probab.,1991

3. On reflecting diffusion processes and Skorokhod decompositions;Chen, Zhen Qing;Probab. Theory Related Fields,1993

4. Gaugeability and conditional gaugeability;Chen, Zhen-Qing;Trans. Amer. Math. Soc.,2002

5. Analytic characterization of conditional gaugeability for non-local Feynman-Kac transforms;Chen, Zhen-Qing;J. Funct. Anal.,2003

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