engleski

Asymptotic behaviour of sharp Sobolev constants in thin domains

In this paper we study the asymptotic behaviour of the constants in Sobolev inequalities in thin domains with respect to the thickness of the domain \eps. We prove that the sharp Sobolev constants in thin domains converge to the sharp Sobolev constant on the lower-dimensional domain, as \eps tends to zero.

Sobolev inequality; Variational characterization; Two-scale convergence; Thin domains

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