Stable phase transitions: from nonlocal to local | Vidéo | Carmin.tv

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Stable phase transitions: from nonlocal to local

By Joaquim Serra

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

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).

Information about the video

Date of recording 12/12/2018
Date of publication 14/01/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19483203
Cite this video 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

Domain(s)

Analysis of PDEs

Bibliography

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

MSC codes

Document(s)

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

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