APPLIED MATH SEMINAR

Title: Optimal Sobolev Extensions
Speaker: Arie Israel, Mathematics, Princeton
When/where: Tuesday, February 8th, 4:15 PM, AKW 200

abstract:
In this talk we discuss the problem of computing a real-valued function F on the plane
taking specified values f(x) for each x in some finite subset E, and with Sobolev norm
lying within an order of magnitude of least possible - such an F is called an optimal Sobolev extension of f.
This is a basic question in the interpolation of data.
For the Sobolev ``norm'' given by the Lp norm of the Hessian of F, we will show how to construct such an extension.
Our method follows a popular approach in extension theory: we cut the extension problem on E into a family of local extension problems on subsets of E;
each local extension problem is solved, and the solutions are glued together using a partition of unity.