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

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The first author is supported by NSF grant 8206400077
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  • 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.

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


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