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

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 r...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 441; no. 1; pp. 194 - 210
Main Authors Galise, G., Koike, S., Ley, O., Vitolo, A.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2016
Elsevier
Subjects
Analysis of PDEs
Comparison principles
Entire solutions
Fully nonlinear elliptic equations
Mathematics
Osserman functions
Viscosity solutions
Comparison principles
Fully nonlinear elliptic equations
Osserman functions
Entire solutions
Viscosity solutions
comparison principles
entire solutions
viscosity solutions
Online AccessGet full text
ISSN0022-247X
1096-0813
1096-0813
DOI10.1016/j.jmaa.2016.03.083

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Summary: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.
ISSN:0022-247X
1096-0813
1096-0813
DOI:10.1016/j.jmaa.2016.03.083