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

Bonfiglioli, Andrea; Lanconelli, Ermanno

Geodesic

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Dirichlet problem with

L^{p}

-boundary data in contractible domains of Carnot groups

Bonfiglioli, Andrea ; Lanconelli, Ermanno

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 579-610

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Résumé

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.

Zbl

Classification : 35J70, 35H20, 31B05, 31C15, 43A80

@article{ASNSP_2006_5_5_4_579_0,
     author = {Bonfiglioli, Andrea and Lanconelli, Ermanno},
     title = {Dirichlet problem with $L^p$-boundary data in contractible domains of {Carnot} groups},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {579--610},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {4},
     year = {2006},
     zbl = {1170.35429},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_579_0/}
}

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Bonfiglioli, Andrea; Lanconelli, Ermanno. Dirichlet problem with $L^p$-boundary data in contractible domains of Carnot groups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 579-610. http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_579_0/