A NOTE ON THE TRACE THEOREM FOR DOMAINS WHICH ARE LOCALLY SUBGRAPH OF A HOLDER CONTINUOUS FUNCTION

作者：Muha Boris^*

来源：Networks and Heterogeneous Media, 2014, 9(1): 191-196.

DOI：10.3934/nhm.2014.9.191

• Trace Theorem
• fluid-structure interaction
• Sobolev spaces
• non-Lipschitz domain

The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a Holder continuous function. More precisely, let eta epsilon C-0,C-alpha (omega), 0 %26lt; alpha %26lt; 1 and let Omega(eta) be a domain which is locally subgraph of a function eta. We prove that mapping gamma(eta) : u (bar right arrow) u (x, eta (x)) an be extended by continuity to a linear, continuous mapping from H-1 (Omega(eta)) to H-s(omega), s %26lt; alpha/2. This study is motivated by analysis of fluid-structure interaction problems.

• 出版日期2014-3