Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term

G. Galise, Shigeaki Koike, O. Ley, A. Vitolo

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper we consider second order fully nonlinear operators with an additive superlinear gradient term. Like in the pioneering paper of Brezis for the semilinear case, we obtain the existence of entire viscosity solutions, defined in all the space, without assuming global bounds. A uniqueness result is also obtained for special gradient terms, subject to a convexity/concavity type assumption where superlinearity is essential and has to be handled in a different way from the linear case.

Original languageEnglish
Pages (from-to)194-210
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume441
Issue number1
DOIs
Publication statusPublished - 2016 Sep 1
Externally publishedYes

Fingerprint

Fully Nonlinear Elliptic Equations
Gradient Term
Entire Solution
Viscosity
Concavity
Fully Nonlinear
Nonlinear Operator
Viscosity Solutions
Semilinear
Convexity
Uniqueness
Entire

Keywords

  • Comparison principles
  • Entire solutions
  • Fully nonlinear elliptic equations
  • Osserman functions
  • Viscosity solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term. / Galise, G.; Koike, Shigeaki; Ley, O.; Vitolo, A.

In: Journal of Mathematical Analysis and Applications, Vol. 441, No. 1, 01.09.2016, p. 194-210.

Research output: Contribution to journalArticle

Galise, G. ; Koike, Shigeaki ; Ley, O. ; Vitolo, A. / Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term. In: Journal of Mathematical Analysis and Applications. 2016 ; Vol. 441, No. 1. pp. 194-210.
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