Global free-boundary regularity for the Signorini problem

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• Alessio Figalli (UT Austin)
• Monday 07 December 2015, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact Prof. Neshan Wickramasekera.

Obstacle problems are an important class of free-boundary problems. The general setting is the following: Given an unknown pair $(u,\Omega)$ where $u$ solves a ``nice’’ equation inside $\Omega$ and has some behavior across $\partial\Omega$, understand the regularity of both $u$ and $\partial \Omega$. The Signorini problem, also known as the ``lower dimensional obstacle problem’’, is a classical problem in this area. While the regularity of the solution is now well understood, the regularity of the free boundary is a much more challenging questions. In this talk I’ll give an overview of the problem and present some recent results on this topic.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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