English
Some new inequalities for the Cheeger constant
Post-edited
Auteurs : Fragalà, Ilaria (Auteur de la Conférence)
CIRM (Editeur )
35A15 - Variational methods
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
49Q10 - Optimization of shapes other than minimal surfaces
52A10 - Convex sets in $2$ dimensions (including convex curves)
52A40 - Inequalities and extremum problems
52B60 - Isoperimetric problems for polytopes
Ressources complémentaires :
http://www.cirm-math.fr/ProgWeebly/Renc1489/Fragala.pdf
CIRM (Editeur )
Résumé :
We discuss some new results for the Cheeger constant in dimension two, including:
- a polygonal version of Faber-Krahn inequality;
- a reverse isoperimetric inequality for convex bodies;
- a Mahler-type inequality in the axisymmetric setting;
- asymptotic behaviour of optimal partition problems.
Based on some recent joint works with D.Bucur,
and for the last part also with B.Velichkov and G.Verzini.
Codes MSC : - a polygonal version of Faber-Krahn inequality;
- a reverse isoperimetric inequality for convex bodies;
- a Mahler-type inequality in the axisymmetric setting;
- asymptotic behaviour of optimal partition problems.
Based on some recent joint works with D.Bucur,
and for the last part also with B.Velichkov and G.Verzini.
35A15 - Variational methods
35P15 - Estimation of eigenvalues and upper and lower bounds for PD operators
49Q10 - Optimization of shapes other than minimal surfaces
52A10 - Convex sets in $2$ dimensions (including convex curves)
52A40 - Inequalities and extremum problems
52B60 - Isoperimetric problems for polytopes
Ressources complémentaires :
http://www.cirm-math.fr/ProgWeebly/Renc1489/Fragala.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2016 Date de captation : 23/11/16 Sous collection : Research talks arXiv category : Analysis of PDEs ; Metric Geometry ; Optimization and Control Domaine : Control Theory & Optimization ; Geometry ; PDE Format : MP4 (.mp4) - HD Durée : 00:41:06 Audience : Researchers Download : https://videos.cirm-math.fr/2016-11-23_Fragala.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Shape optimization and isoperimetric and functional inequalities / Optimisation de formes et inégalités isopérimétriques et fonctionnellesOrganisateurs de la rencontre : Bucur, Dorin ; Buttazzo, Giuseppe ; Henrot, Antoine ; Pratelli, Aldo Dates : 21/11/16 - 25/11/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1489.html
Données de citation
DOI : 10.24350/CIRM.V.19094703Citer cette vidéo: Fragalà, Ilaria (2016). Some new inequalities for the Cheeger constant. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19094703 URI : http://dx.doi.org/10.24350/CIRM.V.19094703 |
Voir aussi
- [Multi angle] Regularity of the optimal sets for spectral functionals. Part I: sum of eigenvalues / Auteur de la Conférence Terracini, Susanna.
- [Multi angle] On the stability of the Bossel-Daners inequality / Auteur de la Conférence Trombetti, Cristina.
- [Multi angle] A minimaxmax problem for improving the torsional stability of rectangular plates / Auteur de la Conférence Gazzola, Filippo.
- [Multi angle] Isoperimetry with density / Auteur de la Conférence Morgan, Frank.
Bibliographie
- Bucur, D., & Fragalà, I. (2016). A Faber-Krahn inequality for the Cheeger constant of N-gons. The Journal of Geometric Analysis, 26(1), 88-117 - http://dx.doi.org/10.1007/s12220-014-9539-5
