Flat minimizers of the Willmore functional: Euler-Lagrange equations
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Submission date: 18. Jul. 2008 (revised version: July 2009)
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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.