Report on Whitney Problems Workshop

Motivated by boundary value problems for partial differential equations, classical trace and extension theorems characterize traces of spaces of generalized smoothness (e.g., Sobolev, Besov, etc.) to smooth submanifolds of a Euclidean space. But in many cases one needs similar results for subsets of a more complicated geometric structure (for instance, after the change of variables initial data may be situated on a Lipschitz surface). The subject is originated from Hassler Whitney seminal papers of 1934 which, in particular, deal with the following problem: given a real function on an arbitrary subset of a Euclidean space to determine whether it is extendible to a function of a prescribed smoothness on the whole of space?