Flat minimizers of the Willmore functional: Euler-Lagrange equations
Péter Hornung · 2008
Let S ⊂ R be a bounded C domain and let g denote the flat metric in R. We prove that there exist minimizers of the Willmore functional restricted to a class of isometric immersions of the Riemannian surface (S, g) into R. 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.