Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations

Abstract

We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The oscillation of nonlinearity $F$ with respect to $x$ is assumed to be small in the $L^{n}$-sense. Here, we employ the Lorentz boundedness of the Hardy-Littlewood maximal operators and an equivalent representation of weighted Lorentz norm.