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Global Lorentz gradient estimates for quasilinear equations with measure data for the strongly singular case: 1 < p ≤ 3n−2 2n−1
Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2020-08-28 , DOI: 10.1142/s021919972050056x
Le Cong Nhan; Le Xuan Truong

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(𝒜(x,u))=μin Ω,u=0on Ω, where μ is a finite signed Radon measure in Ω, Ωn is a bounded domain such that its complement nΩ is uniformly p-thick and 𝒜 is a Carathéodory vector-valued function satisfying growth and monotonicity conditions for the strongly singular case 1<p3n22n1. Our result extends the earlier results [19,22] to the strongly singular case 1<p3n22n1 and a recent result [18] by considering rough conditions on the domain Ω and the nonlinearity 𝒜.

更新日期:2020-09-18

 

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