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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:441

Article

Galise, G.¹  Koike, S.²  Ley, O.³  Vitolo, A.¹ 

[1] Univ Salerno, Salerno, Italy

[2] Tohoku Univ, Sendai, Miyagi 980, Japan

[3] INSA Rennes, IRMAR Inst Rech Math Rennes, Rennes, France

关键词: Fully nonlinear elliptic equations;    Osserman functions;    Comparison principles;    Entire solutions;    Viscosity solutions;   

DOI  :  10.1016/j.jmaa.2016.03.083

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free