Mathematical Sciences - Harold J. Gay Lecture - "Regularity of Interfaces in Phase Transition via Obstacle Problems" by Prof. Dr. Alessio Figalli Professor and Chair, ETH, Zurich, Switzerland) - SL104

Tuesday, February 20, 2018
4:00 pm to 5:30 pm
Floor/Room #: 

Speaker: Alessio Figalli Professor and Chair ETH, Zurich, Switzerland 
Title: Regularity of Interfaces in Phase Transition via Obstacle Problems

Abstract: The so-called Stefan problem describes the
temperature distribution in a homogeneous
medium undergoing a phase change—for example,
ice passing to water—and one aims to describe the
regularity of the interface separating the two
phases. • In its stationary version, the Stefan
problem can be reduced to the classical obstacle
problem, which consists in finding the equilibrium
position of an elastic membrane whose boundary is
held fixed and that is constrained to lie above a
given obstacle. • The aim of this talk is to give a
general overview of the classical theory of the
obstacle problem, and then discuss some very
recent developments on the optimal regularity of
the free boundary both in the static and the
parabolic settings.