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On the $ C^{1,\alpha}$ regularity of $ p$-harmonic functions in the Heisenberg group


Author: Diego Ricciotti
Journal: Proc. Amer. Math. Soc. 146 (2018), 2937-2952
MSC (2010): Primary 35H20, 35J70
DOI: https://doi.org/10.1090/proc/13961
Published electronically: February 8, 2018
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Abstract: We present a proof of the local Hölder regularity of the horizontal derivatives of weak solutions to the $ p$-Laplace equation in the Heisenberg group $ \mathbb{H}^1$ for $ p>4 $.


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Additional Information

Diego Ricciotti
Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
Email: dir17@pitt.edu

DOI: https://doi.org/10.1090/proc/13961
Keywords: Heisenberg group, $p$-Laplace equation, regularity.
Received by editor(s): June 24, 2016
Received by editor(s) in revised form: December 30, 2016, and September 15, 2017
Published electronically: February 8, 2018
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2018 American Mathematical Society

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