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# Maximum Principles for Subharmonic Functions Via Local Semi-Dirichlet Forms

Published:2008-08-01
Printed: Aug 2008
• Kazuhiro Kuwae
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## Abstract

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: positivity preserving form, semi-Dirichlet form, Dirichlet form, subharmonic functions, superharmonic functions, harmonic functions, weak maximum principle, strong maximum principle, irreducibility, absolute continuity condition
 MSC Classifications: 31C25 - Dirichlet spaces 35B50 - Maximum principles 60J45 - Probabilistic potential theory [See also 31Cxx, 31D05] 35J - unknown classification 35J53C - unknown classification 53C58 - unknown classification 58