Regularity for the fully nonlinear parabolic thin obstacle problem

Georgiana Chatzigeorgiou

Regularity for the fully nonlinear parabolic thin obstacle problem

Analysis of PDEs 2021-01-22 v2

Authors: Georgiana Chatzigeorgiou

Abstract

We prove $C^{1, \alpha}$ regularity (in the parabolic sense) for the viscosity solution of a boundary obstacle problem with a fully nonlinear parabolic equation in the interior. Following the method which was first introduced for the harmonic case by L. Caffarelli in 1979, we extend the results of I. Athanasopoulos (1982) who studied the linear parabolic case and the results of E. Milakis and L. Silvestre (2008) who treated the fully nonlinear elliptic case.

Keywords

regularity for elliptic equations regularity of solutions parabolic partial differential equations

Cite

@article{arxiv.1904.09132,
  title  = {Regularity for the fully nonlinear parabolic thin obstacle problem},
  author = {Georgiana Chatzigeorgiou},
  journal= {arXiv preprint arXiv:1904.09132},
  year   = {2021}
}

Comments

In this version funding/grant information has been updated, no other changes applied; 22 pages. Accepted for publication in Commun. Contemp. Math

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