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.

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.

Classification : 35J70, 35H20, 31B05, 31C15, 43A80
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     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},
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     zbl = {1170.35429},
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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://www.numdam.org/item/ASNSP_2006_5_5_4_579_0/

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