The existence of a smooth interface in the evolutionary elliptic Muskat--Verigin problem with nonlinear source

Sergey P. Degtyarev

The existence of a smooth interface in the evolutionary elliptic Muskat--Verigin problem with nonlinear source

Analysis of PDEs 2013-07-03 v2

Authors: Sergey P. Degtyarev

Abstract

We study the two-phase Muskat--Verigin free-boundary problem for elliptic equations with nonlinear sources. The existence of a smooth solution and a smooth free boundary is proved locally in time by applying the parabolic regularization of a condition on the free boundary.

Keywords

Muskat--Verigin problem free-boundary problem elliptic equations nonlinear sources smooth interface parabolic regularization existence

Cite

@article{arxiv.1307.0109,
  title  = {The existence of a smooth interface in the evolutionary elliptic Muskat--Verigin problem with nonlinear source},
  author = {Sergey P. Degtyarev},
  journal= {arXiv preprint arXiv:1307.0109},
  year   = {2013}
}

Comments

This is an English translation of the article S.P. Degtyarev, The existence of a smooth interface in the Muskat-Verigin elliptic evolution problem with a nonlinear source, http://www.ams.org/mathscinet-getitem?mr=2809065

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