The singular set in the Stefan problem

Joaquim Serra (ETH Zürich)

23-Oct-2020, 12:30-13:30 (3 years ago)

Abstract: The Stefan problem, dating back to the XIX century, aims to describe the evolution of a solid-liquid interface, typically a block of ice melting in water. A celebrated work of Luis Caffarelli from the 1970’s established that the ice-water interface must be an analytic surface outside of a certain closed set: the so-called singular set. This singular set was only known to be contained in a surface of class $C^1 $ and it could be, a priori, as large as the regular set. I will present a recent joint work with A. Figalli and X. Ros-Oton in which we obtain new delicate bounds on the size (Hausdorff dimension) of the singular set in the Stefan problem.

Mathematics

Audience: researchers in the discipline


Barcelona Mathematical Days 2020

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Organizers: Amadeu Delshams, Núria Fuster, Marc Masdeu*, Josep Vives
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