@article{c4f5a5e448a44868853e34395ec501c7,
title = "On the two-state problem for general differential operators",
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 [Formula presented]-bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting.",
keywords = "Compensated compactness, Differential inclusions, Rigidity",
author = "{De Philippis}, Guido and Luca Palmieri and Filip Rindler",
note = "Funding Information: G. D. P. is supported by the MIUR SIR -grant “Geometric Variational Problems” ( RBSI14RVEZ ). This project has received funding from the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation programme (grant agreement 757254 ) for the project “SINGULARITY”. F. R. also acknowledges the support from an EPSRC Research Fellowship on “Singularities in Nonlinear PDEs” ( EP/L018934/1 ). Funding Information: G. D. P. is supported by the MIUR SIR-grant ?Geometric Variational Problems? (RBSI14RVEZ). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 757254) for the project ?SINGULARITY?. F. R. also acknowledges the support from an EPSRC Research Fellowship on ?Singularities in Nonlinear PDEs? (EP/L018934/1). Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",
year = "2018",
month = dec,
doi = "10.1016/j.na.2018.03.015",
language = "English (US)",
volume = "177",
pages = "387--396",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Ltd",
}