The 8th Whitney Problems Workshop
October 19 – 23, 2015
Motivated by boundary value problems for partial differential equations, classical trace and extension theorems characterize traces of spaces of generalized smoothness such as Sobolev and Besov to smooth submanifolds of Euclidean space.  The subject originated from Hassler Whitney seminal papers of 1934, which deal with the following problem: given a real function on an arbitrary subset of Euclidean space, determine whether it is extendible to a function of a prescribed smoothness on the entire space.

Whitney developed important analytic and geometric techniques that allowed him to solve this problem for functions defined on subsets of the real line to be extended to m-times continuously differentiable functions on the entire real line. He also formulated and solved similar problems related to jets of functions defined on a subset of Euclidean space in any dimension. In the decades since Whitney’s seminal work, fundamental progress was made by Georges Glaeser, Yuri Brudnyi, Pavel Shvartsman, Edward Bierstone, Pierre Milman, Wieslaw Pawlucki, and Charlie Fefferman.

It is natural also to consider similar extension and trace problems for functions in Sobolev spaces. These results are at a much earlier stage, though there has been significant progress of late. Another problem is to find the Lipschitz constant associated to m-jets.

The objective of the program is bringing together an international group of experts in the areas of function theory and functional and geometric analysis to report on and discuss recent progress and open problems in the area of Whitney type problems.

Scientific Committee

Alex Brudnyi (University of Calgary)
Charles Fefferman (Princeton University)
Erwan Le Gruyer (IRMAR et INSA de Rennes)
Pavel Shvartsman (Technion, Israel Institute of Technology)
Nahum Zobin (College of William and Mary, Williamsburg)

Organizing Committee

Matthew Hirn (ENS Paris)
Erwan Le Gruyer (IRMAR et INSA de Rennes)
Andreea Nicoara (University of Pennsylvania)


On Bernstein Classes of Well Approximable Maps
On the Sundberg Approximation Theorem

The convex paradigm in optimization: dynamical considerations

A transmission problem across a fractal interface

Whitney problems survey
Whitney problems and real algebraic geometry

Computing minimal interpolants in C1,1(Rd)

On the (q, p)-Poincaré inequality, when q < p

Measure density and extension of Besov and Triebel– Lizorkin functions

Interpolation of data in Sobolev spaces

Vectorial Calculus of Variations in L infinity and generalised solutions for fully nonlinear PDE systems

Curve-rational functions

Extremal Extension for $m$-jets of one variable with range in a Hilbert space

A decomposition of functions and weighted Korn in- equality on John domains

Interpolation by Nonnegative Functions

Direct proof of termination of the Kohn algorithm in the real-analytic case

Ck -extendability criterion for functions on a closed set defin- able in any polynomially bounded o-minimal structure

Markov-type inequalities

A Whitney-type extension theorem for jets generated by Sobolev functions

Two weight norm inequalities for singular and fractional integral operators in Rn

Rational approximation of singular functions

  • Nahum Zobin (College of William and Mary, Williamsburg)

Some duality considerations in Whitney problems