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.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2021-03-01
|
| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.161/ |
| _version_ | 1797651570296356864 |
|---|---|
| author | Conti, Sergio Garroni, Adriana |
| author_facet | Conti, Sergio Garroni, Adriana |
| author_sort | Conti, Sergio |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T16:17:43Z |
| format | Article |
| id | doaj.art-d7d09b639fd949b4ab4af122becb73b8 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:17:43Z |
| publishDate | 2021-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-d7d09b639fd949b4ab4af122becb73b82023-10-24T14:18:40ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-03-01359215516010.5802/crmath.16110.5802/crmath.161Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl resultConti, Sergio0Garroni, Adriana1Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, GermanyUniversity of Rome, Sapienza, P.le A. Moro 2, 00185 Rome, ItalyIn 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.161/rigidity estimatesdiv-curl systemsKorn inequalityplasticityincompatible fieldsHodge decomposition |
| spellingShingle | Conti, Sergio Garroni, Adriana Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result Comptes Rendus. Mathématique rigidity estimates div-curl systems Korn inequality plasticity incompatible fields Hodge decomposition |
| title | Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result |
| title_full | Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result |
| title_fullStr | Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result |
| title_full_unstemmed | Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result |
| title_short | Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result |
| title_sort | sharp rigidity estimates for incompatible fields as a consequence of the bourgain brezis div curl result |
| topic | rigidity estimates div-curl systems Korn inequality plasticity incompatible fields Hodge decomposition |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.161/ |
| work_keys_str_mv | AT contisergio sharprigidityestimatesforincompatiblefieldsasaconsequenceofthebourgainbrezisdivcurlresult AT garroniadriana sharprigidityestimatesforincompatiblefieldsasaconsequenceofthebourgainbrezisdivcurlresult |