On the fully nonlinear Alt-Phillips equation

Yijing Wu; Hui Yu

On the fully nonlinear Alt-Phillips equation

Analysis of PDEs 2020-11-18 v2

Authors: Yijing Wu , Hui Yu

Abstract

For a parameter $\gamma\in(1,2)$ , we study the fully nonlinear version of the Alt-Phillips equation, $F(D^2u)=u^{\gamma-1}$ , for $u\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.

Keywords

semilinear elliptic equations parabolic equations partial differential equations

Cite

@article{arxiv.2008.06567,
  title  = {On the fully nonlinear Alt-Phillips equation},
  author = {Yijing Wu and Hui Yu},
  journal= {arXiv preprint arXiv:2008.06567},
  year   = {2020}
}

Comments

20 pages; Typos corrected; New references included; Accepted by IMRN

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