SEMINARIO EDP UAM-ICMAT

Modica type estimates and curvature results for overdetermined elliptic problems

Ponente: Jing Wu (UAM)

Fecha: Viernes, 15 de marzo de 2024 - 12:30

Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM

Resumen:

In this talk, we will establish a Modica type estimate for bounded solutions of the overdetermined elliptic problem. The case of equality will be discussed, too. We will also give some information about the curvature of the boundary. The proof uses the maximum principle together with scaling and contradiction arguments. This is a joint work with David Ruiz and Pieralberto Sicbaldi.

SEMINARIO EDP UAM-ICMAT

A mean field approach for the double curvature prescription problem

Ponente: Luca Battaglia (Università degli Studi Roma Tre)

Fecha: Viernes, 15 de marzo de 2024 - 13:45

Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM

Resumen:

We establish a new mean field-type formulation to study the problem of prescribing Gaussian and geodesic curvature on compact surfaces, which is equivalent to a Liouville-type PDE with nonlinear Neumann conditions. We provide three different existence results in the case of positive, zero and negative Euler characteristics. Based on a joint work with Rafael Lopez-Soriano (Universidad de Granada).