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On the two-state problem for general differential operators (1803.09302v1)
Published 25 Mar 2018 in math.AP
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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