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## A note on the Trace Theorem for domains which are locally subgraph of a H\" older continuous function

Muha, Boris
A note on the Trace Theorem for domains which are locally subgraph of a H\" older continuous function // Networks and heterogeneous media, 9 (2014), 1; 191-196 doi:10.3934/nhm.2014.9.191 (međunarodna recenzija, članak, znanstveni)

Naslov
A note on the Trace Theorem for domains which are locally subgraph of a H\" older continuous function

Autori
Muha, Boris

Izvornik
Networks and heterogeneous media (1556-1801) 9 (2014), 1; 191-196

Ključne riječi
Trace Theorem; Fluid-structure interaction; Sobolev spaces; non-Lipschitz domain.

Sažetak
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 $\gamma_{; ; ; ; \eta}; ; ; ; :u\mapsto u({; ; ; ; \bf x}; ; ; ; , \eta({; ; ; ; \bf x}; ; ; ; ))$ 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 fluid-structure interaction problems.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
037-0693014-2765 - Matematička analiza kompozitnih i tankih struktura (Zvonimir Tutek, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Boris Muha, (267374)

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus