Let be a sub-laplacian on a stratified Lie group . In this paper we study the Dirichlet problem for with -boundary data, on domains which are contractible with respect to the natural dilations of . 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.
@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://www.numdam.org/item/ASNSP_2006_5_5_4_579_0/}
}
TY - JOUR AU - Bonfiglioli, Andrea AU - Lanconelli, Ermanno TI - Dirichlet problem with $L^p$-boundary data in contractible domains of Carnot groups JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 DA - 2006/// SP - 579 EP - 610 VL - Ser. 5, 5 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2006_5_5_4_579_0/ UR - https://zbmath.org/?q=an%3A1170.35429 LA - en ID - ASNSP_2006_5_5_4_579_0 ER -
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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