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

Franchi, Bruno

doi:10.1090/S0002-9947-1991-1040042-8

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

Trans. Amer. Math. Soc. 327 (1991), 125-158

DOI: https://doi.org/10.1090/S0002-9947-1991-1040042-8

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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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