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Research Article | Open Access

Global gradient estimates in directional homogenization

Department of Mathematics Education, Kangwon National University, Chuncheon 24341, Republic of Korea
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Abstract

In this research, we investigate a higher regularity result in periodic directional homogenization for divergence-form elliptic systems with discontinuous coefficients in a bounded nonsmooth domain. The coefficients are assumed to have small bounded mean oscillation (BMO) seminorms and the domain has the δ-Reifenberg property. Under these assumptions we derive global uniform Calderón-Zygmund estimates by proving that the gradient of the weak solution is as integrable as the given nonhomogeneous term.

Keywords

directional homogenizationuniform estimateCalderón-Zygmund theoryReifenberg domainBMO coefficient
CLC number: 35B27, 35J47, 35D30, 35B65

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 27643-27658
DOI: 10.3934/math.20231414

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Cite this article:
Jang Y. Global gradient estimates in directional homogenization. AIMS Mathematics, 2023, 8(11): 27643-27658. https://doi.org/10.3934/math.20231414

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Received: 11 July 2023
Revised: 18 September 2023
Accepted: 25 September 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)