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 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, 35B50, 60J45, 35J, 53C, 58 show english descriptions Dirichlet spaces
Maximum principles
Probabilistic potential theory [See also 31Cxx, 31D05]
unknown classification 35J
unknown classification 53C
unknown classification 58 31C25 - Dirichlet spaces
35B50 - Maximum principles
60J45 - Probabilistic potential theory [See also 31Cxx, 31D05]
35J - unknown classification 35J
53C - unknown classification 53C
58 - unknown classification 58

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