Calculus of Variations and Geometric Measure Theory
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Q. H. Nguyen

Gradient estimates for singular quasilinear elliptic equations with measure data

created by nguyen on 23 May 2017
modified on 25 May 2017

[BibTeX]

Submitted Paper

Inserted: 23 may 2017
Last Updated: 25 may 2017

Year: 2017
Doi: https://arxiv.org/abs/1705.07440

ArXiv: 1705.07440 PDF

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 $\Omega$

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