Free boundary regularity in the Stefan problem

Abstract: The Stefan problem describes phase transitions, such as ice melting to water. In its simplest formulation, this problem consists of finding the evolution of the temperature off the water when a block of ice is submerged inside.

In this talk, I will first discuss the classical theory for this problem. Then I will present some recent results concerning the fine regularity properties of the interface separating water and ice (the so called "free boundary"). As we shall see, these results provide us with a very refined understanding of the Stefan problem's singularities, and they answer some long-standing open questions in the field.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

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NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

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