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

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

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.

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Veröffentlicht in:Comptes rendus. Mathématique 2021-03, Vol.359 (2), p.155-160
Hauptverfasser: Conti, Sergio, Garroni, Adriana
Format: Artikel
Sprache:eng
Schlagworte:
div-curl systems
Hodge decomposition
incompatible fields
Korn inequality
plasticity
rigidity estimates
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Beschreibung
Zusammenfassung: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.
ISSN:1778-3569
1778-3569
DOI:10.5802/crmath.161