Global gradient estimates in directional homogenization

Yunsoo Jang; Yunsoo Jang

doi:10.3934/math.20231414

AIMS Mathematics

2023, Volume 8, Issue 11: 27643-27658. doi: 10.3934/math.20231414

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Global gradient estimates in directional homogenization

Yunsoo Jang ^,

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

Received: 11 July 2023 Revised: 18 September 2023 Accepted: 25 September 2023 Published: 07 October 2023
MSC : 35B27, 35J47, 35D30, 35B65

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 $ \delta $-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.
- directional homogenization,
- uniform estimate,
- Calderón-Zygmund theory,
- Reifenberg domain,
- BMO coefficient
Citation: Yunsoo Jang. Global gradient estimates in directional homogenization[J]. AIMS Mathematics, 2023, 8(11): 27643-27658. doi: 10.3934/math.20231414

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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 $ \delta $-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.

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