# Global free-boundary regularity for the Signorini problem

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

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 and Partial Differential Equations seminar series.