Vol. 14, No. 2, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
$C^{1,\alpha}$-regularity for variational problems in the Heisenberg group

Shirsho Mukherjee and Xiao Zhong

Vol. 14 (2021), No. 2, 567–594
Abstract

We study the regularity of minima of scalar variational integrals of p-growth, 1 < p < , in the Heisenberg group and prove the Hölder continuity of horizontal gradient of minima.

Keywords
Heisenberg groups, $p$-Laplacian, weak solutions, regularity, subelliptic equations
Mathematical Subject Classification 2010
Primary: 35H20, 35J70
Milestones
Received: 3 October 2018
Revised: 1 October 2019
Accepted: 21 November 2019
Published: 20 March 2021
Authors
Shirsho Mukherjee
Department of Mathematics and Statistics
University of Jyväskylä
Jyväskylä
Finland
Xiao Zhong
Department of Mathematics and Statistics
University of Helsinki
Helsinki
Finland