A note on the Liouville theorem of fully nonlinear elliptic equations

Dongsheng Li; Lichun Liang

A note on the Liouville theorem of fully nonlinear elliptic equations

Analysis of PDEs 2025-02-03 v1

Authors: Dongsheng Li , Lichun Liang

Abstract

In this paper, a new method is presented to investigate the asymptotic behavior of solutions to the fully nonlinear uniformly elliptic equation $F(D^2u)=0$ in exterior domains. This method does not depend on the $C^2$ regularity of $F$ and the dimension $n$ .

Keywords

fully nonlinear elliptic equation Liouville theorem asymptotic behavior exterior domain uniform ellipticity

Cite

@article{arxiv.2501.19075,
  title  = {A note on the Liouville theorem of fully nonlinear elliptic equations},
  author = {Dongsheng Li and Lichun Liang},
  journal= {arXiv preprint arXiv:2501.19075},
  year   = {2025}
}

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