Traces of Non-regular Vector Fields on Lipschitz Domains

Abstract

In this note, for Lipschitz domains $\Omega \subset \mathbb{R}^n$ I propose to show the boundedness of the trace operator for functions from H¹(Ω) to L²(∂Ω) as well as for square integrable vector fields in L² with square integrable divergence and curl satisfying a half boundary condition. Such results already exist in the literature. The originality of this work lies on the control of the constants involved. The proofs are based on integration by parts formulas applied to the right expressions.

Mathematics Subject Classification (2010). Primary 35B65; Secondary 35J56.