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

Jun Chen; Xuemei Deng

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

Analysis of PDEs 2023-10-13 v1

Authors: Jun Chen , Xuemei Deng

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.

Keywords

elliptic equations divergence form discontinuous coefficients domains with corners piecewise estimates regularity

Cite

@article{arxiv.2310.08297,
  title  = {Elliptic Equations in Divergence Form with Discontinuous Coefficients in Domains with Corners},
  author = {Jun Chen and Xuemei Deng},
  journal= {arXiv preprint arXiv:2310.08297},
  year   = {2023}
}

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