Speaker
Sergio Conti
Description
Given a Sobolev map from a Lipschitz subset U of an oriented, compact manifold M into another oriented, compact manifold N of the same dimension, we construct an approximation by a C^{1,\alpha} map with a uniform bound on its W^{2,m} norm, for every m>1. The W^{1,p}-distance between the approximation and the original map is controlled in terms of the L^p-deviation from being an isometry, with optimal scaling.
This approximation result is closely connected to geometric rigidity properties, which have played a central role in many developments in nonlinear elasticity over recent decades. The talk is based on joint work with Georg Dolzmann (Regensburg) and Stefan Müller (Bonn).