Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of p-growth

Abstract

We prove a global mixed-norm gradient estimate in the framework of anisotropic Lorentz spaces to general elliptic equations of $p$-growth under weak regularity data. It is assumed that the principle coefficients are small BMO seminorm in $x$-variable, and the boundary of underlying domain is locally $C^{0,1}$-smooth with a small Lipschitz constant.