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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations


Author: Bruno Franchi
Journal: Trans. Amer. Math. Soc. 327 (1991), 125-158
MSC: Primary 35J70; Secondary 35B45
MathSciNet review: 1040042
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Abstract: In this paper we prove a Sobolev-Poincaré inequality for a class of function spaces associated with some degenerate elliptic equations. These estimates provide us with the basic tool to prove an invariant Harnack inequality for weak positive solutions. In addition, Hölder regularity of the weak solutions follows in a standard way.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1040042-8
PII: S 0002-9947(1991)1040042-8
Article copyright: © Copyright 1991 American Mathematical Society