Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: 1 < p ≤ 3 n-2 2 n-1

Abstract

In this paper, we study the global regularity estimates in Lorentz spaces for gradients of solutions to quasilinear elliptic equations with measure data of the form-div((x,?u)) = μin ω,u = 0on ?ω, where μ is a finite signed Radon measure in ω, ω ? ?n is a bounded domain such that its complement ?n?ω is uniformly p-thick and is a Caratheódory vector-valued function satisfying growth and monotonicity conditions for the strongly singular case 1 < p ≤ 3n-2 2n-1. Our result extends the earlier results [19,22] to the strongly singular case 1 < p ≤ 3n-2 2n-1 and a recent result [18] by considering rough conditions on the domain ω and the nonlinearity.