14 papers · 1 filter
Regularity of capillarity droplets with obstacle
Guido De Philippis, Nicola Fusco, Massimiliano Morini
In this paper we study the regularity properties of -minimizers of the capillarity energy in a half space with the wet part constrained to be confined inside a given planar regi…
Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries
Guido De Philippis, Max Engelstein, Luca Spolaor +1
We prove that for minimizers of the vectorial Alt-Caffarelli functional the two-phase singular set of the free boundary is rectifiable and the blow-up is unique almost everywhere o…
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…
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…
Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch +1
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first…