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Asymptoptic behaviour of Sobolev constants for thin curved rods or pipes
Marušić, Sania
2002
Abstract
We study the Sobolev imbedding inequality in a curved rod or pipe
with a smooth central curve $\gamma$. Using the variational approach
and the two-scale convergence for thin domains we find the limit of
the Sobolev imbedding constant W$^{1,r}\hookrightarrow L^{q}$ as
$\epsilon$, the ratio between cross section diameter and the lenght
of the rod, tends to 0.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
34 (2002)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Sania Marušić, "Asymptoptic behaviour of Sobolev constants for thin curved rods or pipes", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 34 (2002), pp. 57-65.
Languages
en
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