English

On the two-state problem for general differential operators

Analysis of PDEs 2018-03-28 v1

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

Keywords

Cite

@article{arxiv.1803.09302,
  title  = {On the two-state problem for general differential operators},
  author = {Guido De Philippis and Luca Palmieri and Filip Rindler},
  journal= {arXiv preprint arXiv:1803.09302},
  year   = {2018}
}
R2 v1 2026-06-23T01:04:26.442Z