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Upper and lower bounds for some shape functionals
Virtualconference
Authors : Buttazzo, Giuseppe (Author of the conference)
CIRM (Publisher )
35J20 - Variational methods for second-order, elliptic equations
49Q10 - Optimization of shapes other than minimal surfaces
35D30 - Weak solutions of PDE
CIRM (Publisher )
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Abstract :
The relations between some quantities related to the Laplace operator are considered. In particular, principal eigenvalue and torsional rigidity are studied in the class of general domains, convex domains, and domains with a small thickness. This allows to obtain a detailed description of the Blasche-Santaló diagram of the two quantities. Several open questions are discussed, in particular when the Laplacian is replaced by the $p$-Laplacian.
MSC Codes : 35J20 - Variational methods for second-order, elliptic equations
49Q10 - Optimization of shapes other than minimal surfaces
35D30 - Weak solutions of PDE
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/04/2021 Conference Date : 29/03/2021 Subseries : Research talks arXiv category : Optimization and Control ; Analysis of PDEs Mathematical Area(s) : Analysis and its Applications ; Control Theory & Optimization ; PDE Format : MP4 (.mp4) - HD Video Time : 01:01:12 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-03-29_Buttazo.mp4 
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Information on the Event
Event Title : Shape Optimization, Spectral Geometry and Calculus of Variations / Optimisation de forme, géométrie spectrale et calcul des variationsEvent Organizers : Bucur, Dorin ; Fragalà, Ilaria ; Henrot, Antoine Dates : 29/03/2021 - 02/04/2021 Event Year : 2021 Event URL : https://conferences.cirm-math.fr/2299.html
Citation Data
DOI : 10.24350/CIRM.V.19738203Cite this video as: Buttazzo, Giuseppe (2021). Upper and lower bounds for some shape functionals. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19738203 URI : http://dx.doi.org/10.24350/CIRM.V.19738203 |
See Also
- [Virtualconference] Sharp inequalities for solutions to elliptic problems with mixed boundary conditions / Author of the conference Trombetti, Cristina.
- [Virtualconference] The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript / Author of the conference Polterovich, Iosif.
- [Virtualconference] Spectrum of the Möbius strip: true, fake and not-so-fake / Author of the conference Krejcirik, David.
Bibliography
- BUTTAZZO, Giuseppe et SHRIVASTAVA, Harish. Optimal shapes for general integral functionals. Annales Henri Lebesgue, 2020, vol. 3, p. 261-272. - http://dx.doi.org/10.5802/ahl.31
