The use of Almgren’s frequency function in the analysis of free boundaries

Federico Franceschini, ETH Zürich
Fine Hall 314

Almgren’s frequency function is a powerful monotone quantity arising in the regularity theory of minimal surfaces and multi-valued harmonic functions. I will explain how it has been used in the thin obstacle problem and in the obstacle problem in some recent breakthroughs, marking analogies and differences with respect to the theory of minimal surfaces. No prior knowledge of free boundaries will be assumed.