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

Bonfiglioli, Andrea; Lanconelli, Ermanno

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, Volume 5 (2006) no. 4, p. 579-610

Abstract

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 1170.35429

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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {4},
     year = {2006},
     pages = {579-610},
     zbl = {1170.35429},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2006_5_5_4_579_0}
}

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, Volume 5 (2006) no. 4, pp. 579-610. http://www.numdam.org/item/ASNSP_2006_5_5_4_579_0/

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