Peter HornungRegularity results for minimizers of Kirchhoff's plate theory Abstract^MAbstractIn 2001 Friesecke, James and Muler derived Kirchhoff's plate theory as a thin film limit from 3d nonlinear elasticity. The admissible limiting deformations are given by $W^{2,2}$ isometric immersions from a subset of $R2$ into $R3$. The Kirchhoff energy of a limiting deformation $u$ is given by the $L2$-norm of $\nabla2 u$. We derive an optimal regularity result for minimizers of this energy functional within the above class (plus suitable boundary conditions). As a by-product we derive the Euler-Lagrange equations (locally) satisfied by critical points. TUESDAY, October 28, 2008 |