Seminar:
Analysis
Event time:
Thursday, November 14, 2024 - 4:00pm
Location:
KT 207
Speaker:
William Feldman
Speaker affiliation:
University of Utah
Event description:
The Bernoulli free boundary problem is a classical model associated with certain interface problems from applications (capillarity, jet flows), and also arising in shape-optimization problems for Dirichlet eigenfunctions. I will explain a result on the large-scale regularity theory of minimizing (and almost minimizing) one-phase free boundaries in periodic media, and a corresponding Liouville theorem for global minimizing solutions. In a forthcoming work with Farhan Abedin (Lafayette College) we have also obtained analogous results in the two-phase case. If times permits I will also discuss an application to quantitative homogenization in a shape-optimization problem for the principal Dirichlet eigenvalue.
Research Area(s):
Analysis & PDE