On the two-state problem for general differential operators. (December 2018) - De Philippis, Guido; Palmieri, Luca; Rindler, Filip
Abstract: 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 L 1 -bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.