4 papers · 1 filter
Fine properties of functions of bounded deformation -- an approach via linear PDEs
Guido De Philippis, Filip Rindler
In this survey we collect some recent results obtained by the authors and collaborators concerning the fine structure of functions of bounded deformation (BD). These maps are $\mat…
Geometric measure theory and differential inclusions
Camillo De Lellis, Guido De Philippis, Bernd Kirchheim +1
In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifold…
Nonclassical minimizing surfaces with smooth boundary
Camillo De Lellis, Guido De Philippis, Jonas Hirsch
We construct a Riemannian metric on (arbitrarily close to the euclidean one) and a smooth simple closed curve such that the unique area mi…
The Area Blow Up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals
Guido De Philippis, Antonio De Rosa, Jonas Hirsch
In this paper we investigate the "area blow-up" set of a sequence of smooth co-dimension one manifolds whose first variation with respect to an anisotropic integral is bounded. Fol…