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Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinus

1969; Association of the Annals of the Fourier Institute; Volume: 19; Issue: 1 Linguagem: Inglês

10.5802/aif.320

1777-5310

Rose-Marie Hervé, Michel Hervé,

Advanced Mathematical Modeling in Engineering

are shown to enjoy the same properties as in the case d i =b i =c=0, namely: local solutions are a system of harmonic functions satisfying Brelot’s axioms, with superharmonic functions coinciding a.e. with local supersolutions; a maximum principle holds for subharmonic functions majorized by functions in εW 0 1,2 ; the class of superharmonic functions in εW 0 1,2 or W loc 1,2 is stable by sweeping out; finally those potentials which belong to εW 0 1,2 are characterized by finite energies. The main difficulty lies in the fact that the bilinear form 〈Lu,ν〉 is not coercive in general, which implies the failure of the methods used in the case d i =b i =c=0.