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 -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}
}