Displaying similar documents to “Harmonic measures of perforated domains”

Analytic potential theory over the p -adics

Shai Haran (1993)

Annales de l'institut Fourier

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Over a non-archimedean local field the absolute value, raised to any positive power α > 0 , is a negative definite function and generates (the analogue of) the symmetric stable process. For α ∈ ( 0 , 1 ) , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.

Dirichlet problem with L p -boundary data in contractible domains of Carnot groups

Andrea Bonfiglioli, Ermanno Lanconelli (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let ℒ be a sub-laplacian on a stratified Lie group G . In this paper we study the Dirichlet problem for ℒ with L p -boundary data, on domains Ω which are contractible with respect to the natural dilations of G . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for ℒ . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.