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

Giulio Galise (1) , Shigeaki Koike (2) , Olivier Ley (3) , Antonio Vitolo (1)

1 Dipartimento di matematica
2 Tohoku University [Sendai]
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Fully nonlinear elliptic equations; Osserman functions; comparison principles; entire solutions; viscosity solutions

Domaines: Equations aux dérivées partielles [math.AP]

Giulio Galise, Shigeaki Koike, Olivier Ley, Antonio Vitolo. Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term. Journal of Mathematical Analysis and Applications, 2016, 441 (1), pp.194-210. ⟨10.1016/j.jmaa.2016.03.083⟩. ⟨hal-01166915⟩