Blog de la Biblioteca de Matemàtiques i Informàtica

SIMBa: The Signorini problem: overview and recent results

El proper dimecres, 5 d’octubre, se celebrarà una nova xerrada  del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Damià Torres Latorre

Data: Wednesday, October 5th, 2022.
Hora: 12:00, virtual coffee break ; 12:20, talk.
Lloc: UPC (FME) and Zoom
Idioma: English

Títol: The Signorini problem: overview and recent results
Resum: The Signorini problem is a free boundary problem arising from elastostatics, and can also be seen as the counterpart to the obstacle problem when the obstacle has codimension 1. The main questions are understanding the regularity of solutions and the regularity of the free boundary. In the first part of the talk, I will present the problem and discuss some relevant known results.
Then, I will introduce the concept of generic regularity and explain the strategy of Figalli, Ros-Oton and Serra to prove that kind of results in the obstacle problem.
Finally, I will expose my recent result with Fernández-Real about generic regularity in the Signorini problem, and comment briefly on the recent developments that have made it possible.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a `seminari(dot)simba(at)ub(dot)edu`.

SIMBa: Supercritical diffusion: memes, stonks and more

El proper dimecres, 20 d’octubre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Damià Torres Latorre
Universitat: Universitat de Barcelona

Data: Wednesday, October 20th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Supercritical diffusion: memes, stonks and more
Resum: In this talk, I will explain the foundations of the theory of elliptic nonlocal PDE, focusing on the fractional Laplacian, $(-\Delta)^{s}$ a model example, and then some recent results on the supercritical fractional obstacle problem.

The first part will start with the relation of fractional operators to jump-diffusion (Lévy) processes and some physical applications. Then, I will give an overview of the basic properties of solutions and compare them to harmonic functions, and also comment on the Caffarelli-Silvestre extension.

In the second part, I will give an idea of how stock prices can be modelled with a nonlocal parabolic obstacle problem, compare the scaling properties of the problem depending on the value of sand present the main points of a recent work with X. Ros-Oton where we study the regularity of the solutions in the supercritical case.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a `seminari(dot)simba(at)ub(dot)edu`.