Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008



J. Korean Math. Soc. 2023; 60(3): 635-682

Online first article February 23, 2023      Printed May 1, 2023

Copyright © The Korean Mathematical Society.

Gradient type estimates for linear elliptic systems from composite materials

Youchan Kim, Pilsoo Shin

University of Seoul; Kyonggi University


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).

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