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 where $μ$ is a finite signed Radon measure in $Ω$, $Ω⊂ℝn$ is a bounded domain such that its complement $ℝn∖Ω$ is uniformly $p$-thick and $𝒜$ is a Carathéodory vector-valued function satisfying growth and monotonicity conditions for the strongly singular case $1. Our result extends the earlier results [19,22] to the strongly singular case $1 and a recent result [18] by considering rough conditions on the domain $Ω$ and the nonlinearity $𝒜$.

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