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Proceedings of the American Mathematical Society

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


Authors: Zhen-Qing Chen and Tusheng Zhang
Journal: Proc. Amer. Math. Soc. 142 (2014), 2135-2149
MSC (2010): Primary 60H15; Secondary 93E20, 35R60
Published electronically: March 13, 2014
MathSciNet review: 3182031
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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.


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Additional Information

Zhen-Qing Chen
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195
Email: zqchen@uw.edu

Tusheng Zhang
Affiliation: Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
Email: tusheng.zhang@manchester.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2014-11907-1
Received by editor(s): March 14, 2012
Received by editor(s) in revised form: May 3, 2012, and June 25, 2012
Published electronically: March 13, 2014
Additional Notes: The first author’s research was partially supported by NSF Grants DMS-0906743 and DMR-1035196.
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2014 Zhen-Qing Chen and Tusheng Zhang