Geodesic
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 Cet article a éte moissonné depuis la source Numdam

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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.

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},
     year = {2006},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 5},
     number = {4},
     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/