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Maximum Principles for Subharmonic Functions Via Local Semi-Dirichlet Forms

Published online by Cambridge University Press:  20 November 2018

Kazuhiro Kuwae*
Affiliation:
Department of Mathematics and Engineering, Faculty of Engineering, Kumamoto University, Kumamoto, 860-8555, Japan e-mail:[email protected]
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Abstract

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Maximum principles for subharmonic functions in the framework of quasi-regular local semi-Dirichlet forms admitting lower bounds are presented. As applications, we give weak and strong maximum principles for (local) subsolutions of a second order elliptic differential operator on the domain of Euclidean space under conditions on coefficients, which partially generalize the results by Stampacchia.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2008

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