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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

Let be a sub-laplacian on a stratified Lie group G . In this paper we study the Dirichlet problem for 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 . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.

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