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Some new inequalities for the Cheeger constant
Post-edited
Authors : Fragalà, Ilaria (Author of the conference)
CIRM (Publisher )
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
Additional resources :
http://www.cirm-math.fr/ProgWeebly/Renc1489/Fragala.pdf
CIRM (Publisher )
Abstract :
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.
MSC Codes : - 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
Additional resources :
http://www.cirm-math.fr/ProgWeebly/Renc1489/Fragala.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 01/12/2016 Conference Date : 23/11/16 Subseries : Research talks arXiv category : Analysis of PDEs ; Metric Geometry ; Optimization and Control Mathematical Area(s) : Control Theory & Optimization ; Geometry ; PDE Format : MP4 (.mp4) - HD Video Time : 00:41:06 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-11-23_Fragala.mp4 
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Information on the Event
Event Title : Shape optimization and isoperimetric and functional inequalities / Optimisation de formes et inégalités isopérimétriques et fonctionnellesEvent Organizers : Bucur, Dorin ; Buttazzo, Giuseppe ; Henrot, Antoine ; Pratelli, Aldo Dates : 21/11/16 - 25/11/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1489.html
Citation Data
DOI : 10.24350/CIRM.V.19094703Cite this video as: 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 |
See Also
- [Multi angle] Regularity of the optimal sets for spectral functionals. Part I: sum of eigenvalues / Author of the conference Terracini, Susanna.
- [Multi angle] On the stability of the Bossel-Daners inequality / Author of the conference Trombetti, Cristina.
- [Multi angle] A minimaxmax problem for improving the torsional stability of rectangular plates / Author of the conference Gazzola, Filippo.
- [Multi angle] Isoperimetry with density / Author of the conference Morgan, Frank.
Bibliography
- 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
