Global Maximal Regularity for Equations with Degenerate Weights

2022/01/10 by Anna Kh. Balci, Sun‐Sig Byun, Balci, Anna Kh. +5 · 1 citation
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2201.03524

Abstract

In this paper we are concerned with global maximal regularity estimates for elliptic equations with degenerate weights. We consider both the linear case and the non-linear case. We show that higher integrability of the gradients can be obtained by imposing a local small oscillation condition on the weight and a local small Lipschitz condition on the boundary of the domain. Our results are new in the linear and non-linear case. We show by example that the relation between the exponent of higher integrability and the smallness parameters is sharp even in the linear or the unweighted case.

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