On the Regularity of p-Harmonic Functions in the Heisenberg Group

Giuseppe Mingione; Zatorska-Goldstein Anna; Xiao Zhong

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 1, page 243-253
  • ISSN: 0392-4041

Abstract

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We describe some recent results obtained in [29], where we prove regularity theorems for sub-elliptic equations in (horizontal) divergence form defined in the Heisenberg group, and exhibiting polynomial growth of order p. The main result tells that when p [ 2 , 4 ) solutions to possibly degenerate equations are locally Lipschitz continuous with respect to the intrinsic distance. In particular, such result applies to p-harmonic functions in the Heisenberg group. Explicit estimates are obtained, and eventually applied to obtain the suitable Calderón-Zygmund theory for the associated non-homogeneous problems.

How to cite

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Mingione, Giuseppe, Anna, Zatorska-Goldstein, and Zhong, Xiao. "On the Regularity of p-Harmonic Functions in the Heisenberg Group." Bollettino dell'Unione Matematica Italiana 1.1 (2008): 243-253. <http://eudml.org/doc/290476>.

@article{Mingione2008,
abstract = {We describe some recent results obtained in [29], where we prove regularity theorems for sub-elliptic equations in (horizontal) divergence form defined in the Heisenberg group, and exhibiting polynomial growth of order p. The main result tells that when $p \in [2,4)$ solutions to possibly degenerate equations are locally Lipschitz continuous with respect to the intrinsic distance. In particular, such result applies to p-harmonic functions in the Heisenberg group. Explicit estimates are obtained, and eventually applied to obtain the suitable Calderón-Zygmund theory for the associated non-homogeneous problems.},
author = {Mingione, Giuseppe, Anna, Zatorska-Goldstein, Zhong, Xiao},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {243-253},
publisher = {Unione Matematica Italiana},
title = {On the Regularity of p-Harmonic Functions in the Heisenberg Group},
url = {http://eudml.org/doc/290476},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Mingione, Giuseppe
AU - Anna, Zatorska-Goldstein
AU - Zhong, Xiao
TI - On the Regularity of p-Harmonic Functions in the Heisenberg Group
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/2//
PB - Unione Matematica Italiana
VL - 1
IS - 1
SP - 243
EP - 253
AB - We describe some recent results obtained in [29], where we prove regularity theorems for sub-elliptic equations in (horizontal) divergence form defined in the Heisenberg group, and exhibiting polynomial growth of order p. The main result tells that when $p \in [2,4)$ solutions to possibly degenerate equations are locally Lipschitz continuous with respect to the intrinsic distance. In particular, such result applies to p-harmonic functions in the Heisenberg group. Explicit estimates are obtained, and eventually applied to obtain the suitable Calderón-Zygmund theory for the associated non-homogeneous problems.
LA - eng
UR - http://eudml.org/doc/290476
ER -

References

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