Sharp free boundary regularity in obstacle problems
Sharp free boundary regularity in obstacle problems
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Alessio Figalli, ETH Z眉rich
The so-called Stefan problem听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.
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In its stationary version, the Stefan problem reduces to the classical obstacle problem, which听consists in finding the equilibrium position of an听elastic membrane whose boundary is held fixed, and that is constrained听to lie above a given obstacle.听
The aim of this talk is to听discuss some very recent developments on the听optimal regularity of the free boundary both in the static and the parabolic setting.