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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark on the Harnack inequality for non-self-adjoint evolution equations


Author: Roger Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 2163-2173
MSC (2000): Primary 58G11; Secondary 53C21, 58G30
Published electronically: November 30, 2000
MathSciNet review: 1825930
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Abstract:

In this paper we consider a non-self-adjoint evolution equation on a compact Riemannian manifold with boundary. We prove a Harnack inequality for a positive solution satisfying the Neumann boundary condition. In particular, the boundary of the manifold may be nonconvex and this gives a generalization to a theorem of Yau.


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Additional Information

Roger Chen
Affiliation: Department of Mathematics, National Cheng Kung University, Tainan, Taiwan
Email: rchen@mail.ncku.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05799-3
PII: S 0002-9939(00)05799-3
Keywords: Harnack inequality, evolution equation, interior rolling R-ball
Received by editor(s): May 27, 1999
Received by editor(s) in revised form: November 2, 1999
Published electronically: November 30, 2000
Additional Notes: This research was partially supported by a grant from NSC
Communicated by: Bennett Chow
Article copyright: © Copyright 2000 American Mathematical Society