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arXiv · 2305.07634

Sobolev estimates for singular-degenerate quasilinear equations beyond the $A_2$ class

Hongjie Dong·Tuoc Phan·Yannick Sire
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Abstract

We study a conormal boundary value problem for a class of quasilinear elliptic equations in bounded domain $\Omega$ whose coefficients can be degenerate or singular of the type $\text{dist}(x, \partial \Omega)^\alpha$, where $\partial \Omega$ is the boundary of $\Omega$ and $\alpha \in (-1, \infty)$ 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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Hongjie Dong, Tuoc Phan, Yannick Sire. 2023-05-12. Sobolev estimates for singular-degenerate quasilinear equations beyond the $A_2$ class. https://arxiv.org/abs/2305.07634

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