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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
Kazuhiro Kuwae*
Affiliation:
Department of Mathematics and Engineering, Faculty of Engineering, Kumamoto University, Kumamoto, 860-8555, Japan e-mail:kuwae@gpo.kumamoto-u.ac.jp
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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.

Keywords

31C2535B5060J4535J53C58positivity preserving formsemi-Dirichlet formDirichlet formsubharmonic functionssuperharmonic functionsharmonic functionsweak maximum principlestrong maximum principleirreducibilityabsolute continuity conditionGirsanov transformationKato class functionDynkin class functionHardy class function
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 4 , 01 August 2008 , pp. 822 - 874
Copyright
Copyright © Canadian Mathematical Society 2008

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