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

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
Description
Summary: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.
ISSN:2640-3501

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