Título: Higher order elliptic boundary regularity and free boundaries

Ponente: Daniel E. Restrepo Montoya (University of Texas at Austin)

Fecha: jueves 28 de abril, 17:00
Lugar: Aula 520, Dpto. de Matemáticas UAM

Online: https://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).