Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular Nonlinearity

2024/05/06 by Mallick, Mohan, Verma, Ram Baran
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.03791

Abstract

In this article we consider the following boundary value problem \ \beginaligned F(x,u,Du,D²u)+c(x)u+ p(x)u^-αamp;=0~in~Ω
uamp;=0~~on~~∂Ω, \endaligned . where Ω is a bounded and C² smooth domain in ℝ^N and F has superlinear growth in gradient and c(c)<-c₀ for some positive constant c₀. Here, we studies the boundary behaviour of the solutions to above equation and establishes the global regularity result similar to one established in [12,16] with linear growth in gradient.

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