Calculus of Variations and Geometric Measure Theory

S. Conti - A. Garroni

Sharp rigidity estimates for incompatible fields as consequence of the Bourgain Brezis div-curl result

created by garroni on 18 Sep 2020
modified by garroni1 on 24 Mar 2022


Published Paper

Inserted: 18 sep 2020
Last Updated: 24 mar 2022

Journal: C. R. Math. Acad. Sci. Paris
Volume: 359
Pages: 155-160
Year: 2021

ArXiv: 2009.08384 PDF


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.