Coloquio información

Coloquio Junior de matemáticas (ICMAT-UAM-UC3M-UCM)

Higher order elliptic boundary regularity and free boundaries

Ponente:  Daniel E. Restrepo Montoya (University of Texas at Austin)
Fecha:  jueves 28 de abril de 2022 - 17:00
Lugar:  Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Online:  youtu.be/XMSkAQdmH5Q

Resumen:

The goal of this talk is to illustrate how to deduce higher order regularity for free boundaries appearing naturally in elliptic problems. In doing so, I will introduce a strategy developed (more or less) recently by many authors (e.g., Ros-Oton and Serra, DeSilva and Savin) that combines blow-up arguments with Liouville-type theorems to derive boundary Harnack inequalities. As a concrete example, I will discuss an ongoing project with Xavi Ros-Oton where we have managed to adapt these ideas to a family of variational problems that interpolate between the Bernoulli one phase problem and the obstacle problem (also known in the literature as the Alt-Phillips free boundary problems).