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

Andrea Bonfiglioli; Ermanno Lanconelli

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 4, page 579-610
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Bonfiglioli, Andrea, and Lanconelli, Ermanno. "Dirichlet problem with L$^{\hbox{p}}$-boundary data in contractible domains of Carnot groups." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.4 (2006): 579-610. <http://eudml.org/doc/242212>.

@article{Bonfiglioli2006,
abstract = {Let $\{\mathcal \{L\}\}$ be a sub-laplacian on a stratified Lie group $\{G\}$. In this paper we study the Dirichlet problem for $\{\mathcal \{L\}\}$ with $L^p$-boundary data, on domains $\Omega $ 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 $\{\mathcal \{L\}\}$. A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.},
author = {Bonfiglioli, Andrea, Lanconelli, Ermanno},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {579-610},
publisher = {Scuola Normale Superiore, Pisa},
title = {Dirichlet problem with L$^\{\hbox\{p\}\}$-boundary data in contractible domains of Carnot groups},
url = {http://eudml.org/doc/242212},
volume = {5},
year = {2006},
}

TY - JOUR
AU - Bonfiglioli, Andrea
AU - Lanconelli, Ermanno
TI - Dirichlet problem with L$^{\hbox{p}}$-boundary data in contractible domains of Carnot groups
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2006
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 4
SP - 579
EP - 610
AB - Let ${\mathcal {L}}$ be a sub-laplacian on a stratified Lie group ${G}$. In this paper we study the Dirichlet problem for ${\mathcal {L}}$ with $L^p$-boundary data, on domains $\Omega $ 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 ${\mathcal {L}}$. A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.
LA - eng
UR - http://eudml.org/doc/242212
ER -

References

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