Generic smoothness in free boundary problems
speaker: Joaquim Serra (ETH Zuerich)abstract: The obstacle problem is one of the most classical free boundary problems. It finds one of its important applications in the (almost two century old) Stefan problem describing the evolution of ice-water interphases. The Signorini problem, also known as "thin obstacle problem", in another very famous free boundary problem from linear elasticity. The talk will explain recent results on the fine structure of the singular set for the classical obstacle problem. We will also discuss how we can prove generic regularity for the Stefan problem in 3D through a precise enough analysis of the singular set for the parabolic obstacle problem. This can be done exploiting a recently discovered deep link between the classical obstacle problem and the Signorini problem, that we will describe. The content of the talk will be based on a recent join work with A. Figalli, and on a forthcoming join work with A. Figalli and X. Ros-Oton.
timetable:
Wed 6 Jun, 11:30 - 12:30, Aula Dini
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