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arXiv · 2310.08297

Elliptic Equations in Divergence Form with Discontinuous Coefficients in Domains with Corners

Jun Chen·Xuemei Deng
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Abstract

We study the equations in divergence form with piecewise $C^{\ga}$ coefficients. The domains contain corners and the discontinuity surfaces are attached to edges of the corners. We obtain piecewise $C^{1,\ga}$ estimates across the discontinuity surfaces and provide an example to illustrate the issue about the regularity at the corners.

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Jun Chen, Xuemei Deng. 2023-10-12. Elliptic Equations in Divergence Form with Discontinuous Coefficients in Domains with Corners. https://arxiv.org/abs/2310.08297

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