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.

Entire solutions of fully nonlinear elliptic equations with asuperlinear gradient term / Galise, Giulio; S., Koike; O., Ley; A., Vitolo. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 441:(2016), pp. 194-210. [10.1016/j.jmaa.2016.03.083]

Entire solutions of fully nonlinear elliptic equations with asuperlinear gradient term

GALISE, GIULIO;
2016

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.
2016
Fully nonlinear elliptic equations; osserman functions; comparison principles; entire solutions; viscosity solutions
01 Pubblicazione su rivista::01a Articolo in rivista
Entire solutions of fully nonlinear elliptic equations with asuperlinear gradient term / Galise, Giulio; S., Koike; O., Ley; A., Vitolo. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 441:(2016), pp. 194-210. [10.1016/j.jmaa.2016.03.083]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/871088
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