Matrix Weights and Regularity for Degenerate Elliptic Equations

2023/02/04 by Giuseppe Di Fazio, Di Fazio, Giuseppe, Maria Stella Fanciullo +7
Mathematics · #35B65 #35J60 #35J70 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2302.02220

openalex publication_date 2023/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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-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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