Calculus of Variations and Geometric Measure Theory

G. De Philippis - L. Palmieri - F. Rindler

On the two-state problem for general differential operators

created by dephilipp on 21 Mar 2018
modified on 05 Jun 2023


Accepted Paper

Inserted: 21 mar 2018
Last Updated: 5 jun 2023

Journal: Nonlinear Anal.
Year: 2018

ArXiv: 1803.09302 PDF


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 the rigidity for approximate solutions to the two-state inclusion with incompatible states for merely $\mathrm{L}^1$-bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.