A three line proof for traces of H1 functions on special Lipschitz domains

TL;DR

This paper presents a concise proof demonstrating that H1 functions defined on Lipschitz domains possess well-defined L2 traces on the boundary, simplifying understanding of boundary behavior in Sobolev spaces.

Contribution

The paper introduces a significantly shorter proof for the existence of L2 traces of H1 functions on Lipschitz domains, improving proof efficiency.

Findings

H1 functions on Lipschitz domains have L2 boundary traces

The proof is notably shorter than existing proofs

Boundary trace properties are clarified and simplified

Abstract

We give a very short proof of the fact that H1 functions on Lipschitz domains have L2 traces on the boundary of the domain.