One day in PDEs
in honor of Sandro Salsa
October 1st, 2021 Politecnico di Milano
It will be possible to attend all the talks either in Aula Rogers or in streaming
To access aula Rogers you will need a valid COVID-19 green pass

Lectures:
Luis Caffarelli (UTexas, Austin) - online
Donatella Danielli (ASU, Phoenix) - online
Alessio Figalli (ETH, Zurich) - online
Alfio Quarteroni (Politecnico, Milano) - in Milano

REGISTRATION FORM
Registration is free but mandatory, for organizing purposes
Registration will be open until Wednesday 29th
The Zoom link will be sent to online participants on Thursday 30th

For further information, you can write to onedaypdes-dmat@polimi.it

The aim of this meeting is to gather some of the world's top experts in the field of partial differential equations and their central role in the applications of mathematics. This meeting will provide an opportunity to increase the dissemination of important recent research achievements and to discuss future developments and open problems. Particular attention will be given to the interaction between theoretical and applied mathematics.

## 18:00Closing with Executive Vice Rector prof. Donatella SciutoClosing toast

Luis Caffarelli (UTexas, Austin)
The Interaction of Free Boundary with a Diffusion on a Plane
Donatella Danielli (ASU, Phoenix)
A penalized boundary obstacle problem for the bi-Laplacian
In this talk we are concerned with a two-penalty boundary obstacle problem for the bi-Laplace operator in the upper unit ball. This problem arises in connection with unilateral phenomena for flat elastic plates. It can also be seen as an obstacle-type problem for the fractional Laplacian $(−\Delta)^{3/2}$. Our goals are to establish the well-posedness and the optimal regularity of the solution, and to study the structure of the free boundary. The proofs are based on monotonicity formulas of Almgren- and Monneau-type. This is joint work with Alaa Haj Ali.
Alessio Figalli (ETH, Zurich)
The singular set in the Stefan problem
The Stefan problem describes phase transitions such as ice melting to water, and it is among the most classical free boundary problems. It is well known that the free boundary consists of a smooth part (the regular part) and singular points. In this talk, I will describe a recent result with Ros-Oton and Serra, where we analyze the singular set in the Stefan problem and prove a series of fine results on its structure.
Alfio Quarteroni (Politecnico, Milano)
The Beat of Math
Mathematical models based on first principles allow the description of the blood motion in the human circulatory system, as well as the interaction between electrical, mechanical, and fluid-dynamical processes occurring in the heart. This is a classical environment where multi-physics and multi-scale processes must be addressed.
Appropriate systems of nonlinear differential equations (either ordinary and partial) and efficient numerical strategies must be devised to allow for the analysis of both heart function and dysfunction, and the simulation, control and optimization of therapy and surgery.
This presentation will address some of these issues and a few representative applications of clinical interest.
Acknowledgment: The work presented in this talk is part of the project iHEART that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 740132).

Organizing Committee: