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arXiv · 2407.01062

Planar closed curves with prescribed curvature

Paolo Caldiroli·Anna Capietto
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Abstract

By variational methods, we prove existence of planar closed curves with prescribed curvature for some classes of curvature functions. The main difficulty is to obtain bounded Palais-Smale sequences. This is achieved by adding a parameter in the problem and using a version of the "monotonicity trick" introduced by M. Struwe in 1988.

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Paolo Caldiroli, Anna Capietto. 2024-07-01. Planar closed curves with prescribed curvature. https://doi.org/10.3934/dcds.2024056

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