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

In this article we consider the following boundary value problem equation*abs \ aligned F (x, u, Du, D^{2u) +c (x) u+ p (x) u^-&=0~in~\\ u&=0~~on~~, aligned. equation* where is a bounded and C^2 smooth domain in RN 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.