Inserted: 18 sep 2020
Last Updated: 24 mar 2022
Journal: C. R. Math. Acad. Sci. Paris
In this note we show that a sharp rigidity estimate and a sharp Korn's inequality for matrix-valued fields whose incompatibility is a bounded measure can be obtained as a consequence of a Hodge decomposition with critical integrability due to Bourgain and Brezis.