

Preprint 46/2008
Flat minimizers of the Willmore functional: Euler-Lagrange equations
Peter Hornung
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Submission date: 18. Jul. 2008 (revised version: July 2009)
Pages: 39
Bibtex
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Abstract:
Let be a bounded
domain
and let g denote the flat metric in
.
We prove that there exist minimizers of the Willmore functional restricted
to a class of isometric immersions of the Riemannian surface (S, g)
into
.
We derive the Euler-Lagrange equations satisfied by such constrained
minimizers. Our main motivation comes from nonlinear elasticity, where
this constrained Willmore functional arises naturally and is called
Kirchhoff's plate functional.