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arXiv · 2201.03524

Global Maximal Regularity for Equations with Degenerate Weights

Anna Kh. Balci·Sun-Sig Byun·Lars Diening·Ho-Sik Lee
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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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Anna Kh. Balci, Sun-Sig Byun, Lars Diening, Ho-Sik Lee. 2022-01-10. Global Maximal Regularity for Equations with Degenerate Weights. https://arxiv.org/abs/2201.03524

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