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Boundary value problems for Willmore curves in \(\mathbb {R}^2\). (English) Zbl 1362.53010

Summary: In this paper the Navier problem and the Dirichlet problem for Willmore curves in \(\mathbb {R}^2\) are solved.

MSC:

53A04 Curves in Euclidean and related spaces
34K10 Boundary value problems for functional-differential equations
49Q10 Optimization of shapes other than minimal surfaces
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References:

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