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Sharp inequalities for solutions to elliptic problems with mixed boundary conditions
Virtualconference
Authors : Trombetti, Cristina (Author of the conference)
CIRM (Publisher )
35B45 - A priori estimates
35J05 - Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35B06 - Symmetries, invariants, etc. in context of PDE
CIRM (Publisher )
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Abstract :
We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on L1 comparison) between solutions to an elliptic partial differential equation on a smooth bounded set Ω with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as Ω. This includes for instance mixed problems.
Keywords : a priori estimates; comparison principle; mixed boundary conditions; Robin boundary conditions
MSC Codes : Keywords : a priori estimates; comparison principle; mixed boundary conditions; Robin boundary conditions
35B45 - A priori estimates
35J05 - Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35B06 - Symmetries, invariants, etc. in context of PDE
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/04/2021 Conference Date : 02/04/2021 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : PDE Format : MP4 (.mp4) - HD Video Time : 00:44:44 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2021-04-02_Trombetti.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.19738503Cite this video as: Trombetti, Cristina (2021). Sharp inequalities for solutions to elliptic problems with mixed boundary conditions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19738503 URI : http://dx.doi.org/10.24350/CIRM.V.19738503 |
See Also
- [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.
- [Virtualconference] Upper and lower bounds for some shape functionals / Author of the conference Buttazzo, Giuseppe.
Bibliography
- ALVINO, A., CHIACCHIO, F., NITSCH, C., et al. Sharp estimates for solutions to elliptic problems with mixed boundary conditions. Journal de Mathématiques Pures et Appliquées, 2020. - https://doi.org/10.1016/j.matpur.2020.12.003
