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- W1971851561 abstract "It is shown first that every finely [hyper]harmonic function in an open subset of the plane R 2 is [hyper]harmonic in the usual sense. This depends on a new boundary minimum principle for a bounded domain U in the plane, using fine limits at the boundary, but without making any assumption on the magnitude of the negative part of the given hyperharmonic function u in U. Afterwards this minimum principle is extended to the case where U is just finely open (and bounded) and u finely hyperharmonic. None of these results extends to the spaces R k for k>2. Finally the notion of fine harmonicity is characterized by a property of local approximation by restrictions of usual harmonic functions." @default.
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- W1971851561 date "1974-01-01" @default.
- W1971851561 modified "2023-09-29" @default.
- W1971851561 title "Fonctions harmoniques et fonctions finement harmoniques" @default.
- W1971851561 doi "https://doi.org/10.5802/aif.532" @default.
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