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

Abstract

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

28 pages

References in corpus (1)

• Local Lipschitz regularity for degenerate elliptic systems