A note on the Trace Theorem for domains which are locally subgraph of a Holder continuous function

Abstract

The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\" older continuous function. More precisely, let $\eta \in C^{0,\alpha }(\omega )$, $0<\alpha <1$ and let ${\Omega }_{\eta }$ be a domain which is locally subgraph of a function $\eta$. We prove that mapping ${\gamma }_{\eta }:u\mapsto u(\mathbf{x},\eta (\mathbf{x}))$ can be extended by continuity to a linear, continuous mapping from $H^1({\Omega }_{\eta })$ to $H^s(\omega )$, $s<\alpha /2$. This study is motivated by analysis of fluid-structure interaction problems.

arXiv commentNetworks and Heterogeneous Media

References in corpus (1)

• Global weak solutions for an incompressible Newtonian fluid interacting with a linearly elastic Koiter shell