# Mathematical Sciences Research Institute

Home » A Whitney Extension Theorem for Sobolev spaces

# Seminar

A Whitney Extension Theorem for Sobolev spaces November 09, 2011 (11:30 AM PST - 12:30 PM PST)
Parent Program: -- MSRI: Simons Auditorium
Speaker(s) Arie Israel (University of Texas, Austin)
Description No Description
Video
We will recall classical results in smooth extension theory discovered by Hassler Whitney in the 1930\'s and present the recent construction of a linear extension operator for functions in the Sobolev space $L^{m,p}(R^n)$; that is, a linear operator that takes a real-valued function f defined on a finite subset E of Euclidean space, and produces a function F defined on $R^n$, which matches f on E, and has Sobolev norm minimal to within a factor of $C=C(m,n,p)$. This generalizes work of C.
Fefferman on the extension of $C^m$ functions, and in fact our method gives a new proof of his theorem. Furthermore, a closer analysis of our construction shows that the extension F can be taken to have a simple dependence on f (assisted bounded depth) though, in general, not an even simpler one (bounded depth). This is joint work with C. Fefferman and G.K.