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Giuseppe Di Fazio; Fanciullo, Maria Stella; Dario Daniele Monticelli; Scott, Rodney; Zamboni, Pietro
arXiv (Cornell University), 02/2023Paper, Journal Article
We prove local boundedness, Harnack's inequality and local regularity for weak solutions of quasilinear degenerate elliptic equations in divergence form with Rough coefficients. Degeneracy is encoded by a non-negative, symmetric, measurable matrix valued function Q(x) and two suitable non-negative weight functions. We setup an axiomatic approach in terms of suitable geometric conditions and local Sobolev-Poincaré inequalities. Data integrability is close to L1 and is exploited in terms of a suitable Stummel-Kato class that in some cases is necessary for local regularity.
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