Non standard diffusions in fluids, kinetic equations and probability / Diffusions non standards en mécanique des fluides, équations cinétiques et probabilités

Collection Non standard diffusions in fluids, kinetic equations and probability / Diffusions non standards en mécanique des fluides, équations cinétiques et probabilités

Organisateur(s) Imbert, Cyril ; Mouhot, Clément ; Tristani, Isabelle

Date(s) 10/12/2018 - 14/12/2018

URL associée https://conferences.cirm-math.fr/1862.html

00:00:00 / 00:00:00

3 5

Stable phase transitions: from nonlocal to local

De Joaquim Serra

The talk will review the motivations, state of the art, recent results, and open questions on four very related PDE models related to phase transitions: Allen-Cahn, Peierls-Nabarro, Minimal surfaces, and Nonlocal Minimal surfaces. We will focus on the study of stable solutions (critical points of the corresponding energy functionals with nonnegative second variation). We will discuss new nonlocal results on stable phase transitions, explaining why the stability assumption gives stronger information in presence of nonlocal interactions. We will also comment on the open problems and obstructions in trying to make the nonlocal estimates robust as the long-range (or nonlocal) interactions become short-range (or local).

Informations sur la vidéo

Date de captation 12/12/2018
Date de publication 14/01/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19483203
Citer cette vidéo Serra, Joaquim (12/12/2018). Stable phase transitions: from nonlocal to local. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19483203
URL https://dx.doi.org/10.24350/CIRM.V.19483203

Domaine(s)

Equations aux dérivées partielles

Bibliographie

Cabré, X., Cinti, E., & Serra, J. (2018). Flatness of stable nonlocal phase transitions in in $\mathbb {R}^ 3$, forthcoming preprint
Cabré, X., Cinti, E., & Serra, J. (2017). Stable $s$-minimal cones in $\mathbb {R}^ 3$ are flat for $s\sim 1$.〈arXiv:1710.08722〉 - https://arxiv.org/abs/1710.08722
Cinti, E., Serra, J., & Valdinoci, E. Quantitative flatness results and BV-estimates for nonlocal minimal surfaces, to appear in Journal of Differential Geometry
Dipierro, S., Serra, J., & Valdinoci, E. Improvement of flatness for nonlocal phase transitions, to appear in American Journal of Mathematics
Figalli, A., & Serra, J. (2017). On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1.〈arXiv:1705.02781〉 - https://arxiv.org/abs/1705.02781

Codes MSC

Document(s)

https://www.cirm-math.fr/ProgWeebly/Renc1862/Serra.pdf

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