【online】Euclidean distance function in the presence of an obstacle
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题目: Euclidean distance function in the presence of an obstacle
报告人: Piermarco Cannarsa（University of Rome Tor Vergata）
时间: 2020年11月19日 16:00-17:00
方式: Zoom APP ID：680 9256 2983 密码：472595
摘要：The obstacle problem is a classical topic in analysis, which may take different forms depending on the quantities you observe. In this talk, we are interested in the regularity of the Euclidean distance function from a given point in the presence of a compact obstacle with smooth boundary. First, we will show that the distance is semiconcave with a fractional modulus and that, near the obstacle, such a regularity is optimal. Then, we will show that the distance function is everywhere differentiable (except for the point target) if and only if no obstacle is present. Finally, we will study the propagating structure of the singular set of the distance both at `interior points' and on the boundary of the obstacle. For such an analysis, we will use recent results on the extension of semiconcave functions defined on a closed domain. This is joint work with Paolo Albano and Vincenzo Basco.