Calculus of Variations and Geometric Measure Theory

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
modified on 09 Nov 2019


Accepted Paper

Inserted: 12 feb 2019
Last Updated: 9 nov 2019

Journal: Journal of Functional Analysis
Year: 2019


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 $\frac{3n-2}{2n-1}<p\leq 2-\frac{1}{n}$.