A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with Lipschitz Boundary Values

Abstract

In this note we show that gradient of Harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in $L^p$ for all finite $p\ge 1$.

8 pages, Journal: Glasnik Matematicki

References in corpus (1)

• A New Characterisation of $\infty$-Harmonic and $p$-Harmonic Maps via Affine Variations in $L^{\infty }$