The Willmore boundary problem |
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Authors: | Reiner Schätzle |
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Affiliation: | 1. Mathematisches Institut der Eberhard-Karls-Universit?t Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany
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Abstract: | We consider the Euler–Lagrange equation of the Willmore functional coupled with Dirichlet and Neumann boundary conditions on a given curve. We prove existence of a branched solution, and for Willmore energy < 8π, we prove the existence of a smooth, embedded solution. |
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