On the two-state problem for general differential operators

Guido De Philippis, Luca Palmieri, Filip Rindler

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Pages (from-to)387-396
Number of pages10
JournalNonlinear Analysis, Theory, Methods and Applications
StatePublished - Dec 2018


  • Compensated compactness
  • Differential inclusions
  • Rigidity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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