Planar loops with prescribed curvature via Hardy’s inequality

Gabriele Cora; Roberta Musina

doi:10.4171/nnu90

BooksStandalone TitlesCollected Volumepp. 89–109

Planar loops with prescribed curvature via Hardy’s inequality

Gabriele Cora
Université Libre de Bruxelles, Brussels, Belgium
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Roberta Musina
Università di Udine, Italy

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Abstract

We investigate the existence of closed planar loops with prescribed curvature. Our approach is variational; it relies on a Hardy-type inequality and on its associated functional space.