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Continuity of weak solutions of elliptic partial differential equations

Visa Latvala Department of Mathematics, University of Joensuu

TBD mathscidoc:1701.332995

Arkiv for Matematik, 41, (1), 95-104, 2001.8
The continuity of weak solutions of elliptic partial differential equations $$div \mathcal{A}(x,\nabla u) = 0$$ is considered under minimal structure assumptions. The main result guarantees the continuity at the point$x$_{0}for weakly monotone weak solutions if the structure of$A$is controlled in a sequence of annuli $$B(x_0 ,R_j )\backslash \bar B(x_0 ,r_j )$$ with uniformly bounded ratio$R$_{$j$}$/r$_{$j$}such that lim_{$jā†’āˆž$}$R$_{$j$}=0. As a consequence, we obtain a sufficient condition for the continuity of mappings of finite distortion.
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@inproceedings{visa2001continuity,
  title={Continuity of weak solutions of elliptic partial differential equations},
  author={Visa Latvala},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203606216516804},
  booktitle={Arkiv for Matematik},
  volume={41},
  number={1},
  pages={95-104},
  year={2001},
}
Visa Latvala. Continuity of weak solutions of elliptic partial differential equations. 2001. Vol. 41. In Arkiv for Matematik. pp.95-104. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203606216516804.
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