Maximum Principles for Subharmonic Functions Via Local Semi-Dirichlet Forms

Kuwae, Kazuhiro

Canadian journal of mathematics, Tome 60 (2008) no. 4, pp. 822-874

Résumé

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.

Détail

DOI : 10.4153/CJM-2008-036-8

Mots-clés : 31C25, 35B50, 60J45, 35J, 53C, 58, positivity preserving form, semi-Dirichlet form, Dirichlet form, subharmonic functions, superharmonic functions, harmonic functions, weak maximum principle, strong maximum principle, irreducibility, absolute continuity condition, Girsanov transformation, Kato class function, Dynkin class function, Hardy class function

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