On the boundary values of Sobolev $W^1_p$-functions

TL;DR

This paper characterizes the boundary traces of Sobolev spaces $W^1_p( abla)$ for $p>n$ using local oscillations, providing intrinsic boundary descriptions for arbitrary domains.

Contribution

It introduces a new intrinsic characterization of Sobolev boundary traces for $p>n$ based on local oscillations, applicable to any domain.

Findings

Provides boundary trace descriptions for $W^1_p$ with $p>n$

Uses local oscillations for intrinsic characterization

Applicable to arbitrary domains

Abstract

For each $p>n$ we use local oscillations to give intrinsic characterizations of the trace of the Sobolev space $W^1_p(\Omega)$ to the boundary of an arbitrary domain $\Omega\subset R^n$.