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November 2024
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Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
A priori estimates for the 2D one-phase Muskat problem with contact points
13:30
Edoardo Bocchi - Aula Buzano (DISMA Politecnico di Torino)
We address the dynamics of a viscous and incompressible free-surface fluid in a Hele-Shaw cell or,
Date : Thursday, 14 November 2024
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Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
On Courant and Pleijel theorems for sub-Riemannian Laplacians
13:00
Bernard Helffer - Aula Buzano (DISMA Politecnico di Torino)
We are interested in the number of nodal domains of eigenfunctions ofsub-Laplacians on sub-Riemannian manifolds. Specifically, we
Date : Tuesday, 19 November 2024
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Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
Directional maximal and singular integrals
15:00
Francesco Di Plinio - Aula Buzano (DISMA Politecnico di Torino)
This talk is concerned with L^p(R^n) estimates for maximal averaging operators on variable subspaces of codimension d between 1 and n-1, as well as
Date : Thursday, 21 November 2024
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Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
A variational analysis of nematic axisymmetric films
14:30
Giulia Bevilacqua - Aula Buzano (DISMA Politecnico di Torino)
Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. Some variational models
Date : Wednesday, 27 November 2024
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A case study for free boundary regularity: the obstacle problem

Seminari di Analisi Matematica dell'Università e del Politecnico di Torino
Date: Tuesday, 12 December 2023 14:30 - 15:30

Venue: Federico Franceschini - Aula Buzano (DISMA Politecnico di Torino)

Free boundaries arise naturally in many nonlinear elliptic (or parabolic) problems: roughly speaking, free boundaries are interfaces at which solutions display some kind of discontinuous behaviour. Such interfaces are “free” in the sense that they are not prescribed and do not solve themselves an equation. The main (open) problem in the field is to determine if free boundaries are in fact smooth hypersurfaces and what is going on if they are not. A model case is the so-called Obstacle Problem.In this talk  --- aimed to a general Analysis audience --- I will give an introduction to the Obstacle Problem and present the current understanding of the free boundary regularity in this case. I will explain some recent results (obtained with W. Zatoń) concerning the C\infty regularity of the free boundary outside of a lower-dimensional set. Such results bear nice similarities with the regularity theory of Minimal Surfaces.

 

Speaker
Federico Franceschini
Affiliation
ETH Zurigo
Room
Aula Buzano
Proposed by
Alessandro Audrito

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