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FIELD Math:Analysis May 18 (Fri), 2018 14:00-16:00 Kim, Youchan Kim, Soojung 서울시립대학교 Regularity results for elliptic equations from composite materials In this talk, we discuss about global $L^p$-gradient estimates and local piece-wise gradient H\"{o}lder continuity results for elliptic equations from composite materials.First we prove global $L^{p}$-gradient estimates for the weak solutions to linear elliptic equations under the assumption that the domain is composed of a finite number of disjoint Reifenberg flat boundaries while the coefficients have small BMO-semi norms in each subdomain.Also we show local piece-wise gradient H\"{o}lder continuity results for the weak solutions to nonlinear elliptic equations if the domain is composed of a finite number of disjoint $C^{1,\alpha}$-boundaries and the nonlinearities are H\"{o}lder continuous in each subdomain.

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