4 papers · 1 filter
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…
A two-point function approach to connectedness of drops in convex potentials
Michael Goldman, Guido De Philippis
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimise…
On the two-state problem for general differential operators
Guido De Philippis, Luca Palmieri, Filip Rindler
In this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove…
Boundary regularity of mass-minimizing integral currents and a question of Almgren
Camillo De Lellis, Guido De Philippis, Jonas Hirsch +1
This short note is the announcement of a forthcoming work in which we prove a first general boundary regularity result for area-minimizing currents in higher codimension, without a…