Characterization and representation of the lower semicontinuous envelope of the elastica functional Caractérisation et représentation de l’enveloppe semi-continue inférieure de la fonctionnelle de l’elastica
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چکیده
We characterize the lower semicontinuous envelope F of the functional F(E) := ∫∂E [1 + |κ∂E |p]dH1, defined on boundaries of sets E ⊂ R2, where κ∂E denotes the curvature of ∂E and p > 1. Through a desingularization procedure, we find the domain of F and its expression, by means of different representation formulas. 2004 Elsevier SAS. All rights reserved. Résumé On caractérise l’enveloppe semi-continue inférieure F de la fonctionnelle F(E) := ∫∂E[1 + |κ∂E |p]dH1, définie sur la classe des frontières des domaines E ⊂ R2, où κ∂E dénote la courbure de ∂E et p > 1. Grâce à une méthode de désingularisation, on trouve le domaine de F et son expression, à l’aide de différentes formules de représentation. 2004 Elsevier SAS. All rights reserved.
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