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arXiv · 2206.07884

Piecewise smoothness for linear elliptic systems with piecewise smooth coefficients

Youchan Kim
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Abstract

Li and Vogelius, and Li and Nirenberg obtained piecewise $C^{1,\gamma}$-regularity for linear elliptic problems with piecewise $C^{\gamma}$-coefficients which come from composite materials. In this paper, we obtain piecewise $C^{m+1,\gamma}$-regularity for linear elliptic systems with piecewise $C^{m,\gamma}$-coefficients which also come from composite materials. This answers the open problem suggested by Li and Vogelius, and Li and Nirenberg.

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Youchan Kim. 2022-06-16. Piecewise smoothness for linear elliptic systems with piecewise smooth coefficients. https://arxiv.org/abs/2206.07884

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