数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (5): 1583-1590.

• 论文 • 上一篇    下一篇

STRONG COMPARISON PRINCIPLES FOR SOME NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

李岩岩1, 王博2   

  1. 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USA;
    2. Corresponding author. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2018-04-03 出版日期:2018-11-09 发布日期:2018-11-09
  • 作者简介:Yanyan LI,E-mail:yyli@math.rutgers.edu;Bo WANG,E-mail:wangbo89630@bit.edu.cn
  • 基金资助:
    Li was partially supported by NSF grant DMS-1501004. Wang was partially supported by NSFC (11701027).

STRONG COMPARISON PRINCIPLES FOR SOME NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

Yanyan LI1, Bo WANG2   

  1. 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USA;
    2. Corresponding author. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2018-04-03 Online:2018-11-09 Published:2018-11-09
  • Supported by:
    Li was partially supported by NSF grant DMS-1501004. Wang was partially supported by NSFC (11701027).

摘要: In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form ▽2ψ + L(x, ▽ψ), including the conformal hessian operator.

关键词: Hopf lemma, strong comparison principle, degenerate ellipticity, conformal invariance

Abstract: In this paper, we obtain the strong comparison principle and Hopf Lemma for locally Lipschitz viscosity solutions to a class of nonlinear degenerate elliptic operators of the form ▽2ψ + L(x, ▽ψ), including the conformal hessian operator.

Key words: Hopf lemma, strong comparison principle, degenerate ellipticity, conformal invariance