Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

Shigeaki Koike, Olivier Ley

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given.

Original languageEnglish
Pages (from-to)110-120
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume381
Issue number1
DOIs
Publication statusPublished - 2011 Sep 1

Keywords

  • Comparison principle
  • Growth conditions
  • Nonconvex hamiltonians
  • Systems of pDE
  • Viscosity solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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