Regularity for fully nonlinear elliptic equations with natural growth in gradient and singular nonlinearity

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Regularity for fully nonlinear elliptic equations with natural growth in gradient and singular nonlinearity

Year : 2025

Publisher : Academic Press Inc.

Source Title : Journal of Differential Equations

Document Type :

Abstract

In this article, we consider the following boundary value problem: {F(x,u,Du,D2u)+c(x)u+p(x)u−α=0inΩ,u=0on∂Ω, where Ω is a bounded and C2 smooth domain in RN. The operator F is proper and has superlinear growth in gradient. This study examines the boundary behavior of the solutions to the above equation and establishes a global regularity result similar to that established in [11,15], which involves linear growth in the gradient.