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

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.
177, Part B
387
396
https://www.sciencedirect.com/science/article/pii/S0362546X18300737?via%3Dihub
https://arxiv.org/abs/1803.09302
De Philippis, Guido; Palmieri, Luca; Rindler, Filip
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/85686
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