A joint generalization of Whitney's C-1 extension theorem and Aversa-Laczkovich-Preiss' extension theorem

Abstract

We prove a joint generalization of Whitney's C-1 extension theorem and Aversa-Laczkovich-Preiss' extension theorem. It can be roughly described as a theorem on extendibility of a differentiable function defined on a closed subset of R-n to a differentiable function on R-n with preserving the continuity of the derivative.

Other results on C-1 and differentiable extensions from "thick" subsets of R-n are also proved.

Keywords

• Differentiable functions of several variables
• Extensions
• Whitney's extension theorem
• Strict differentiability
• Contingent cone