On the two-state problem for general differential operators

2018/03/25 by Guido De Philippis, De Philippis, Guido, Luca Palmieri +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1803.09302

arxiv created 2018/03/25 · arxiv updated 2018/03/28

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.

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