Calculus of Variations and Geometric Measure Theory

S. Mukherjee - X. Zhong

$C^{1,α}$-Regularity for variational problems in the Heisenberg group

created by mukherjee on 20 Jun 2018
modified on 20 Mar 2021


Published Paper

Inserted: 20 jun 2018
Last Updated: 20 mar 2021

Journal: Analysis & PDE
Volume: 14
Number: 2
Pages: 567–594
Year: 2021
Doi: 10.2140/apde.2021.14.567

ArXiv: 1711.04671 PDF


We study the regularity of minima of scalar variational integrals of $p$-growth, $1<p<\infty$, in the Heisenberg group and prove the H\"older continuity of horizontal gradient of minima.