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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 strong maximum principle for parabolic systems in a convex set with arbitrary boundary


Author: Lawrence Christopher Evans
Journal: Proc. Amer. Math. Soc. 138 (2010), 3179-3185
MSC (2010): Primary 35B50, 35K40; Secondary 35D40
Published electronically: May 13, 2010
MathSciNet review: 2653943
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Abstract: In this paper we prove a strong maximum principle for certain parabolic systems of equations. In particular, our methods place no restriction on the regularity of the boundary of the convex set in which the system takes its values, and therefore our results hold for any convex set. We achieve this through the use of viscosity solutions and their corresponding strong maximum principle.


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Additional Information

Lawrence Christopher Evans
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: lcevans@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10495-1
PII: S 0002-9939(2010)10495-1
Received by editor(s): November 13, 2009
Published electronically: May 13, 2010
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.