On the $C^{1,\alpha }$ regularity of $p$-harmonic functions in the Heisenberg group
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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 $p>4$.References
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Additional Information
- Diego Ricciotti
- Affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260
- MR Author ID: 1143666
- Email: dir17@pitt.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2937-2952
- MSC (2010): Primary 35H20, 35J70
- DOI: https://doi.org/10.1090/proc/13961
- MathSciNet review: 3787355