Coloquio Junior de matemáticas
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 - 17:00Lugar: 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).
