A simple proof of a strong comparison principle for semicontinuous viscosity solutions of the prescribed mean curvature equation

Masaki Ohnuma, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A strong comparison principle for semicontinuous viscosity solutions of the prescribed mean curvature equation is considered. The difficulties of the problem come from the fact that this nonlinear equation is non-uniformly elliptic, does not depend on the value of unknown functions, depends on spatial variables and solutions are semicontinuous. Our simple proof of the strong comparison principle consists only of three ingredients, the definition of viscosity solutions, the inf and sup convolutions of functions, and the theory of classical solutions of quasilinear elliptic equations. Once we have the strong comparison principle, we can prove a weak comparison principle for semicontinuous viscosity solutions of the prescribed mean curvature equation in a bounded domain.

Original languageEnglish
Pages (from-to)180-188
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume181
DOIs
Publication statusPublished - 2019 Apr

Keywords

  • Prescribed mean curvature equation
  • Semicontinuous viscosity solution
  • Strong comparison principle

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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