Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GRADIENT TYPE ESTIMATES FOR LINEAR ELLIPTIC SYSTEMS FROM COMPOSITE MATERIALS

  • Youchan Kim (Department of Mathematics University of Seoul) ;
  • Pilsoo Shin (Department of Mathematics Kyonggi University)
  • Received : 2022.08.23
  • Accepted : 2022.11.08
  • Published : 2023.05.01
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Abstract

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise Hölder continuous but locally Hölder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient Hölder continuity which was obtained by the previous results.

Keywords

Acknowledgement

Y. Kim was supported by the 2019 Research Fund of the University of Seoul. P. Shin was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(No. NRF-2020R1I1A1A01066850).

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