Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group

We examine the geometry of the level sets of particular horizontally p-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the p-capacitary potential of a bounded annulus in the Heisenberg group are strictly starshaped.

Bibliographic Details
Main Authors:	Mattia Fogagnolo, Andrea Pinamonti
Format:	Article
Language:	English
Published:	AIMS Press 2021-03-01
Series:	Mathematics in Engineering
Subjects:	p-laplacian p-harmonic stashaped level sets heisenberg group
Online Access:	http://www.aimspress.com/article/doi/10.3934/mine.2021046?viewType=HTML

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spelling	doaj-53d95fcffcc74db7a7c55db009c54a842021-03-24T01:30:55ZengAIMS PressMathematics in Engineering2640-35012021-03-013611510.3934/mine.2021046Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg groupMattia Fogagnolo 0Andrea Pinamonti11. Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56126 Pisa (PI), Italy2. Università degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), ItalyWe examine the geometry of the level sets of particular horizontally p-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the p-capacitary potential of a bounded annulus in the Heisenberg group are strictly starshaped.http://www.aimspress.com/article/doi/10.3934/mine.2021046?viewType=HTMLp-laplacianp-harmonicstashaped level setsheisenberg group
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mattia Fogagnolo Andrea Pinamonti
spellingShingle	Mattia Fogagnolo Andrea Pinamonti Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group Mathematics in Engineering p-laplacian p-harmonic stashaped level sets heisenberg group
author_facet	Mattia Fogagnolo Andrea Pinamonti
author_sort	Mattia Fogagnolo
title	Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group
title_short	Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group
title_full	Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group
title_fullStr	Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group
title_full_unstemmed	Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group
title_sort	strict starshapedness of solutions to the horizontal p-laplacian in the heisenberg group
publisher	AIMS Press
series	Mathematics in Engineering
issn	2640-3501
publishDate	2021-03-01
description	We examine the geometry of the level sets of particular horizontally p-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the p-capacitary potential of a bounded annulus in the Heisenberg group are strictly starshaped.
topic	p-laplacian p-harmonic stashaped level sets heisenberg group
url	http://www.aimspress.com/article/doi/10.3934/mine.2021046?viewType=HTML
work_keys_str_mv	AT mattiafogagnolo strictstarshapednessofsolutionstothehorizontalplaplacianintheheisenberggroup AT andreapinamonti strictstarshapednessofsolutionstothehorizontalplaplacianintheheisenberggroup
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Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group

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