*Submitted Paper*

**Inserted:** 23 may 2017

**Last Updated:** 25 may 2017

**Year:** 2017

**Doi:** https://arxiv.org/abs/1705.07440

**Abstract:**

In this paper, we prove $L^q$-estimates for gradients of solutions to
singular quasilinear elliptic equations with measure data
$$-\operatorname{div}(A(x,\nabla u))=\mu,$$ in a bounded domain
$\Omega\subset\mathbb{R}^{N}$, where $A(x,\nabla u)\nabla u \asymp

\nabla
u

^p$, $p\in (1,2-\frac{1}{n}]$ and $\mu$ is a Radon measure in $\Omega$