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arXiv · 1803.09302

On the two-state problem for general differential operators

Guido De Philippis·Luca Palmieri·Filip Rindler
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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 $\mathrm{L}^1$-bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.

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Guido De Philippis, Luca Palmieri, Filip Rindler. 2018-03-25. On the two-state problem for general differential operators. https://arxiv.org/abs/1803.09302

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