Abstract

This paper studies a new gradient regularity in Lorentz spaces for solutions to a class of quasilinear divergence form elliptic equations with nonhomogeneous Dirichlet boundary conditions: where (), the nonlinearity A is a monotone Carathéodory vector valued function defined on for and the p-capacity uniform thickness condition is imposed on the complement of our bounded domain Ω. Moreover, for given data , the problem is set up with general Dirichlet boundary data . In this paper, the optimal good-λ type bounds technique is applied to prove some results of fractional maximal estimates for gradient of solutions. And the main ingredients are the action of the cut-off fractional maximal functions and some local interior and boundary comparison estimates developed in previous works [45], [52], [53] and references therein.