Abstract

A free boundary problem is a PDE problem with overdetermined boundary conditions; at the boundary, both the value of u and ∇u are prescribed — or, informally, the domain itself is part of the unknown.
In this talk, I will explain how one can rigorously formulate them, and discuss their challenges and strengths through two paradigmatic examples: the Bernoulli one-phase problem, an elliptic case, and the Stefan problem, a parabolic one.
No prior knowledge of the topic is required.