On the two-state problem for general differential operators. (December 2018)

• Record Type: Journal Article
• Authors: De Philippis, Guido; Palmieri, Luca; Rindler, Filip
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part B
• Page Start: 387
• Page End: 396
• Publication Date: 2018-12
• Subjects: Compensated compactness -- Rigidity -- Differential inclusions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.03.015
• Languages: English
• ISSNs: 0362-546X

Abstract

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 L 1 -bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.