Trace Operator’s Range Characterization for Sobolev Spaces on Lipschitz Domains of $\protect \mathbb{R}^2$

Abstract

We give, first, two new applications related to the range characterization of the range of trace operator in $H^2(\Omega )$. After this, we characterize the range of trace operator in the Sobolev spaces $ W^{3,p}(\Omega )$ when $\Omega $ is a connected bounded domain $\mathbb{R}^2$ with Lipschitz-continuous boundary.