A note on the Trace Theorem for domains which are locally subgraph of a Hölder continuous function
Boris Muha  Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia (email) Abstract: The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a Hölder 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 $\gamma_{\eta}:u\mapsto u({\bf x},\eta({\bf x}))$ 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 fluidstructure interaction problems.
Keywords: Trace Theorem, fluidstructure interaction, Sobolev spaces, nonLipschitz domain.
Received: May 2013; Revised: July 2013; Available Online: April 2014. 
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