Matrix Weights and Regularity for Degenerate Elliptic Equations
Analysis of PDEs
2023-02-07 v1
Abstract
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-Poincar\'e 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.
Cite
@article{arxiv.2302.02220,
title = {Matrix Weights and Regularity for Degenerate Elliptic Equations},
author = {Giuseppe Di Fazio and Maria Stella Fanciullo and Dario Daniele Monticelli and Scott Rodney and Pietro Zamboni},
journal= {arXiv preprint arXiv:2302.02220},
year = {2023}
}