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Hölder continuity for quasilinear subelliptic equations in Carnot Carathéodory spaces
Author(s) -
Di Fazio Giuseppe,
Zamboni Pietro
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310185
Subject(s) - mathematics , carnot cycle , lipschitz continuity , hölder condition , sobolev space , mathematical analysis , lipschitz domain , harnack's inequality , pure mathematics , sobolev inequality , physics , thermodynamics
In this note we prove the Harnack inequality and the Hölder continuity for weak solutions of quasilinear subelliptic equation of the form$$ \sum _{j=1}^{m} X^*_j (x, u(x), Xu(x)) + B(x, u(x), Xu(x)) = 0\, , $$where u belongs to Sobolev spaces with respect to a system of locally Lipschitz vector fields. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)