# Planned seminars

## 30/09/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Rafael D. Benguria, Universidad Católica de Chile

The Gagliardo-Nirenberg-Sobolev (GNS) inequalities have played a major role in applied mathematics and mathematical physics in more than half a century. In this talk I will present several new results concerning the counterparts of the GNS inequalities on bounded domains. Of course concentration of the minimizers of the GNS inequalities is a main tool in the proof of existence of minimizers on bounded domains. Naturally concentration occurs in the interior for Dirichlet boundary conditions and on the boundary for Neumann boundary conditions. In the Neumann case this leaves a set of
interesting open problems depending on the characteristic of the boundary. This is in part joint work with Cristobal Vallejos (Penn State U.) and Hanne Van Den Bosch (U. de Chile) and in part with Soledad Benguria (U. Wisconsin, Madison).

## 07/10/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Monica Clapp, Universidad Nacional Autónoma de México

The Yamabe equation on a Riemannian manifold $(M,g)$ is relevant to the question of finding a constant scalar curvature metric on $M$ that is conformally equivalent to the given one.

An optimal $\ell$-partition for the Yamabe equation is a cover of $M$ by $\ell$ pairwise disjoint open subsets such that the Yamabe equation with Dirichlet boundary condition has a least energy solution on each one of these sets, and the sum of the energies of these solutions is minimal.

We will present some recent results obtained in collaboration with Angela Pistoia (La Sapienza Università di Roma) and Hugo Tavares (Universidade de Lisboa) that establish the existence and qualitative properties of such partitions.

If time allows, we will also present some results on symmetric optimal partitions obtained in collaboration with Angela Pistoia, and with Alberto Saldaña (UNAM) and Andrzej Szulkin (Stockholm University).

## 14/10/2021, Thursday, 16:00–17:00 Europe/Lisbon — Online

Juraj Földes, University of Virginia
To be announced

## 21/10/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Simone Dovetta, Università degli Studi di Roma "La Sapienza"
To be announced