Abstract

The aim of this paper is to develop the regularity theory for a weak solution to a class of quasilinear nonhomogeneous elliptic equations, whose prototype is the following mixed Dirichlet -Laplace equation of type in Lorentz space, with given data , , for and () satisfying a Reifenberg flat domain condition or a -capacity uniform thickness condition, which are considered in several recent papers. To better specify our result, the proofs of regularity estimates involve fractional maximal operators and valid for a more general class of quasilinear nonhomogeneous elliptic equations with mixed data. This paper not only deals with the Lorentz estimates for a class of more general problems with mixed data but also improves the good- approach technique proposed in our preceding works (Tran, 2019; Tran and Nguyen, 2019; Tran and Nguyen, 2020; Tran and Nguyen (in press)), to achieve the global Lorentz regularity estimates for gradient of weak solutions in terms of fractional maximal operators.