Calculus of Variations and Geometric Measure Theory
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Q. H. Nguyen - C. P. Nguyen

Pointwise gradient estimates for a class of singular quasilinear equation with measure data

created by nguyen on 12 Feb 2019

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Submitted Paper

Inserted: 12 feb 2019
Last Updated: 12 feb 2019

Year: 2019

Abstract:

Local and global pointwise gradient estimates are obtained for solutions to the quasilinear elliptic equation with measure data $-\operatorname{div}(A(x,\nabla u))=\mu$ in a bounded and possibly nonsmooth domain $\Omega$ in $\mathbb{R}^n$. Here $\operatorname{div}(A(x,\nabla u))$ is modeled after the $p$-Laplacian. Our results extend earlier known results to the singular case in which $\frac{3n-2}{2n-1}<p\leq 2-\frac{1}{n}$.


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