Global gradient estimates for parabolic systems from composite materials



We obtain global gradient estimates for the weak solutions to parabolic systems from composite materials in Orlicz spaces, which is a new result even for \(L^{p}\)-spaces. We assume that the domain is composed of a finite number of disjoint subdomains with Reifenberg flat boundaries, while the coefficients have small BMO semi-norms in each subdomain and allowed to have big jumps on the boundaries of subdomains. Our proof is based on a new geometric result that for disjoint Reifenberg flat domains \(\Omega ^{k}\) and \(\Omega ^{l}\), the normal vectors at \(P \in \partial \Omega ^{k}\) and \(Q \in \partial \Omega ^{l}\) are almost opposite if P and Q are close enough.

Mathematics Subject Classification

Primary 35K40 Secondary 35B65 



The authors would like to appreciate the referee for the careful reading of this manuscript, and offering valuable comments for this manuscript. Y. Jang was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (No. NRF-2016R1D1A1B03935364). Y. Kim was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (No. NRF-2017R1D1A1B03034302).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Mathematical Analysis and Computation (CMAC)Yonsei UniversitySeoulRepublic of Korea
  2. 2.Department of MathematicsUniversity of SeoulSeoulRepublic of Korea

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