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

2015/06/23 by Giulio Galise, Shigeaki Koike, Galise, Giulio +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1506.06994

arxiv created 2015/06/23 · openalex publication_date 2015/06/23 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• A Schauder regularity theory for nonlocal and mixed local-nonlocal viscous Hamilton\unicodex2013Jacobi equations

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