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The H–1-norm of tubular neighbourhoods of curves

Yves van Gennip;  Mark A. Peletier — 2011

ESAIM: Control, Optimisation and Calculus of Variations

We study the -norm of the function 1 on tubular neighbourhoods of curves in ℝ 2 . We take the limit of small thickness, and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit → 0, containing contributions from the length of the curve (at order ), the ends ( ), and the curvature ( ). The second result is a Γ-convergence result, in which the central curve may vary along the sequence...

The -norm of tubular neighbourhoods of curves

Yves van Gennip;  Mark A. Peletier — 2011

ESAIM: Control, Optimisation and Calculus of Variations

We study the -norm of the function 1 on tubular neighbourhoods of curves in ℝ 2 . We take the limit of small thickness , and we prove two different asymptotic results. The first is an asymptotic development for a fixed curve in the limit → 0, containing contributions from the length of the curve (at order ), the ends ( ), and the curvature ( ). The second result is a Γ-convergence result, in which the central curve may vary along the...

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