On the Regularity of p-Harmonic Functions in the Heisenberg Group
Mingione, Giuseppe ; Anna, Zatorska-Goldstein ; Zhong, Xiao
Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 243-253 / Harvested from Biblioteca Digitale Italiana di Matematica

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.

Descriviamo alcuni recenti risultati ottenuti in [29], dove si dimostrano teoremi di regolarità per soluzioni di equazioni sub-ellittiche in forma di divergenza orizzontale, nel gruppo di Heisenberg. I risultati coprono il caso di operatori a crescita p, come il p-Laplaciano nel gruppo di Heisenberg, e sono ottenuti sotto l'ipotesi adimensionale p[2,4).

Publié le : 2008-02-01
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     author = {Giuseppe Mingione and Zatorska-Goldstein Anna and Xiao Zhong},
     title = {On the Regularity of p-Harmonic Functions in the Heisenberg Group},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1},
     year = {2008},
     pages = {243-253},
     zbl = {1164.35039},
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     url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_1_243_0}
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Mingione, Giuseppe; Anna, Zatorska-Goldstein; Zhong, Xiao. On the Regularity of p-Harmonic Functions in the Heisenberg Group. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 243-253. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_1_243_0/

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