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arXiv · 1902.04414

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

Quoc-Hung Nguyen·Nguyen Cong Phuc
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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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Quoc-Hung Nguyen, Nguyen Cong Phuc. 2019-02-12. Pointwise gradient estimates for a class of singular quasilinear equation with measure data. https://arxiv.org/abs/1902.04414

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