A note on the Trace Theorem for domains which are locally subgraph of a Hölder continuous function
Boris Muha · Networks and Heterogeneous Media · 2014
The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a Hölder continuousfunction. More precisely, let $\eta\in C^{0,\alpha}(\omega)$, $0<\alpha<1$ and let $\Omega_{\eta}$ be a domain which is locally subgraphof a function $\eta$. We prove that mapping $\gamma_{\eta}:u\mapsto u({\bf x},\eta({\bf x}))$ can be extended by continuity to a linear, continuousmapping from $H^1(\Omega_{\eta})$ to $H^s(\omega)$, $s<\alpha/2$. This study is motivated by analysis of fluid-structure interaction problems.