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Minimax Theory and its Applications 04 (2019), No. 1, 087--099
Copyright Heldermann Verlag 2019



Harnack Inequality and Smoothness for some Non Linear Degenerate Elliptic Equations

Giuseppe Di Fazio
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6, 95125 Catania, Italy
difazio@dmi.unict.it

Maria S. Fanciullo
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6, 95125 Catania, Italy
fanciullo@dmi.unict.it

Pietro Zamboni
Dip. di Matematica e Informatica, UniversitÓ di Catania, Viale A. Doria 6, 95125 Catania, Italy
zamboni@dmi.unict.it



We prove Harnack inequality and smoothness for weak solutions of quasilinear degenerate elliptic equation with respect to a system of non commuting vector fields. In addition, the structure assumptions allow quadratic growth in the gradient.

Keywords: Harnack inequality, Muckenhoupt weights, degenerate elliptic equations, Stummel-Kato classes, Hoermander vector fields.

MSC: 35B45, 35B65

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