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, dened 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 a superlinear gradient term

VITOLO, Antonio
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, dened 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4650554
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 13
social impact