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Fields Medal Lecture: Regularity of interfaces in phase transition — Alessio Figalli — ICM2018

Regularity of interfaces in phase transitions via obstacle problems Alessio Figalli Abstract: The so-called Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase change, for example ice melting to water. An important goal is to describe the structure 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 which is constrained to lie above a given obstacle. In this talk I will give a general overview of the classical theory of the obstacle problem, and then discuss recent developments on the structure of interfaces, both in the static and the parabolic settings. ICM 2018 - International Congress of Mathematicians © www.icm2018.org     Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.