Sobolev estimates for singular-degenerate quasilinear equations beyond the A₂ class

2023/05/12 by Hongjie Dong, Dong, Hongjie, Tuoc Phan +3
Computer Science · Mathematics · #35B45 #35D30 #35J62 #35J70 #35J75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.07634

openalex publication_date 2023/05/12 · openalex created_date 2023/05/17 · openalex updated_date 2026/08/01

Abstract

We study a conormal boundary value problem for a class of quasilinear elliptic equations in bounded domain Ω whose coefficients can be degenerate or singular of the type dist(x, ∂ Ω)^α, where ∂ Ω is the boundary of Ω and α∈ (-1, ∞) is a given number. We establish weighted Sobolev type estimates for weak solutions under a smallness assumption on the weighted mean oscillations of the coefficients in small balls. Our approach relies on a perturbative method and several new Lipschitz estimates for weak solutions to a class of singular-degenerate quasilinear equations.

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