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 L1-bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.
On the two-state problem for general differential operators / De Philippis, Guido; Palmieri, Luca; Rindler, Filip. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 177, Part B:(2018), pp. 387-396. [10.1016/j.na.2018.03.015]
On the two-state problem for general differential operators
De Philippis Guido;PALMIERI, LUCA;
2018-01-01
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 L1-bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.| File | Dimensione | Formato | |
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