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 C0,1-smooth with a small Lipschitz constant.