TY - JOUR
T1 - Entire solutions of fully nonlinear elliptic equations with a superlinear gradient term
AU - Galise, G.
AU - Koike, S.
AU - Ley, O.
AU - Vitolo, A.
N1 - Funding Information:
G. Galise and A. Vitolo have been supported by the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni ( GNAMPA 2013 ) of the Istituto Nazionale di Alta Matematica ( INdAM ). S. Koike was supported in part by Grant-in-Aid for Scientific Research (No. 23340028 ) of Japan Society for the Promotion of Science . O. Ley is partially supported by the ANR (Agence Nationale de la Recherche) through HJnet project ANR-12-BS01-0008-01 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - 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.
AB - 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.
KW - Comparison principles
KW - Entire solutions
KW - Fully nonlinear elliptic equations
KW - Osserman functions
KW - Viscosity solutions
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U2 - 10.1016/j.jmaa.2016.03.083
DO - 10.1016/j.jmaa.2016.03.083
M3 - Article
AN - SCOPUS:84962850107
SN - 0022-247X
VL - 441
SP - 194
EP - 210
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -