Vol. 14, No. 2, 2021

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$C^{1,\alpha}$-regularity for variational problems in the Heisenberg group

Shirsho Mukherjee and Xiao Zhong

Vol. 14 (2021), No. 2, 567–594

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.

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