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

Abstract

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.

Keywords

• rigidity estimates
• div-curl systems
• Korn inequality
• plasticity
• incompatible fields
• Hodge decomposition