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Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis

Maria Alessandra Ragusa (1999)

Commentationes Mathematicae Universitatis Carolinae

In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class H 0 1 , p ( Ω ) for all 1 < p < and, as a consequence, the Hölder regularity of the solution u . is an elliptic second order operator with discontinuous coefficients ( V M O ) and the lower order terms belong to suitable Lebesgue spaces.

Étude de l’équation 1 2 Δ u - u μ = 0 μ est une mesure positive

Denis Feyel, A. de La Pradelle (1988)

Annales de l'institut Fourier

On montre que les solutions faibles de l’équation Δ u - u μ = 0 , où μ est une mesure positive négligeant les polaires, vérifient une inégalité de Harnack. On s’occupe également des sursolutions dont on fait la représentation intégrale a l’aide d’une fonction de Green. Comme les solutions sont discontinues, on est amené à utiliser les formules probabilistes.

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