$ W^{1,p} $ estimates for elliptic systems on composite material with almost partially BMO coefficients

Caiyan Li; Dongsheng Li

doi:10.3934/cpaa.2021100

Article Contents

2021, Volume 20, Issue 9: 3143-3159. Doi: 10.3934/cpaa.2021100

This issue Previous Article Moderate deviation principles for unbounded additive functionals of distribution dependent SDEs Next Article Riesz-type representation formulas for subharmonic functions in sub-Riemannian settings

$ W^{1,p} $ estimates for elliptic systems on composite material with almost partially BMO coefficients

Caiyan Li^1, , and
Dongsheng Li^2,

1.
School of Mathematical Sciences, Peking Uinversity, Beijing 100871, China
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

^* Corresponding author
^* Corresponding author

Received: March 31, 2018

Revised: April 30, 2021

Early access: June 2021

Published: September 2021

The first author is supported by NSF grant 8206400077

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Abstract

In this paper, we establish uniform $ W^{1,p} $ estimates for composite material problems which can be described by a divergence form elliptic system on a nonsmooth domain composed of a finite number of subdomains. We want to derive global $ W^{1,p} $ regularity under the assumption that the coefficients are almost $ (\delta,R) $-vanishing of codimension 1 (see Definition 1.2) in each of multiple subdomains and the boundaries of subdomains are Reifenberg flat, moreover the estimates do not depend on the distance between these subdomains.

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Mathematics Subject Classification: Primary: 35D10, 35J30, 35J50; Secondary: 35L30.

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References

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