Journal of the
Korean Mathematical Society JKMS

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 H\"{o}lder continuous but locally H\"{o}lder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient H\"{o}lder continuity which was obtained by the previous results.

Keywords: Linear elliptic systems, smoothness and regularity, composite materials

MSC numbers: Primary 35J47; Secondary 35B65, 74A40

Supported by: 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).