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Displaying similar documents to “A remark on gradients of harmonic functions in dimension ≥3”

Boundary properties of functions with finite Dirichlet integrals

J. L. Doob (1962)

Annales de l'institut Fourier

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L’auteur étudie dans un espace de Green (en particulier un domaine borné de R n ) les fonctions B L D (limites en un certain sens des fonctions assez régulières à intégrale de Dirichlet finie). On se ramène au cas harmonique montré qu’une telle fonction harmonique u est solution d’un problème de Dirichlet-Martin (c’est-à-dire correspond à une donnée u ' sur la frontière de Martin), ce qui entraîne l’existence d’une limite “fine” u ' p.p. Cela résulte de travaux antérieurs et de la remarque que...

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

Marcello Lucia, Michael J. Puls (2015)

Analysis and Geometry in Metric Spaces

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Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.