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math.AP2018
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…
math.AP2018
Relaxation for partially coercive integral functionals with linear growth
Filip Rindler, Giles Shaw
We prove an integral representation theorem for the -relaxation of the functional \[ \mathcal{F}\colon u\mapsto\int_Ωf(x,u(x),\nabla u(x))\;\mathrm{dd…
math.AP2018
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…