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Interfaces and Free Boundaries

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Volume 21, Issue 1, 2019, pp. 87–129
DOI: 10.4171/IFB/418

Published online: 2019-05-09

An obstacle problem for elastic curves: Existence results

Marius Müller[1]

(1) Universität Ulm, Germany

We consider an obstacle problem for elastic curves with fixed ends. We attempt to extend the graph approach provided in [8]. More precisely, we investigate nonexistence of graph solutions for special obstacles and extend the class of admissible curves in a way that an existence result can be obtained by a penalization argument.

Keywords: Obstacle problem, elastic energy, length penalization, convex envelope

Müller Marius: An obstacle problem for elastic curves: Existence results. Interfaces Free Bound. 21 (2019), 87-129. doi: 10.4171/IFB/418