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 - 17:00Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
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).