engleski

Asymptotic Behaviour of Sobolev Constants for Thin Curved rods or Pipes

We study the Sobolev imbedding inequality in a curved rod or a pipe with a smooth central curve \gamma. Using tha variational approach and the two-scale convergence for thin domains we find the limit of the Sobolev imbedding constant W^{;1, r};->L^{;q};. as \eps, the ratio between cross section diameter and the length of the rod, tends to 0.

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

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