Global gradient estimates for very singular quasilinear elliptic equations with measure data

2019/09/16 by Tran, Minh-Phuong, Nguyen, Thanh-Nhan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.06991

Abstract

This paper continues the development of regularity results for quasilinear measure data problems \begincases -div(A(x,∇ u)) amp;= μ in Ω,
u amp;=0 on ∂ Ω, \endcases in Lorentz and Lorentz-Morrey spaces, where Ω⊂ ℝⁿ (n ≥ 2), μ is a finite Radon measure on Ω, and A is a monotone Carathéodory vector valued operator acting between W^1,p₀(Ω) and its dual W^-1,p'(Ω). It emphasizes that this paper studies the `very singular' case 1

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