Calculus of Variations and Geometric Measure Theory

M. Fogagnolo - A. Pinamonti

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

created by pinamonti on 06 Nov 2020
modified on 09 Nov 2020


Accepted Paper

Inserted: 6 nov 2020
Last Updated: 9 nov 2020

Journal: Mathematics in Engineering
Year: 2020

Dedicated to Alberto Farina on the occasion of his 50th birthday


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.