The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables

Abstract

We construct a differentiable function f from R^n to R (n [.gt.] 1) such that the inverse image of B(0,1) under the gradient mapping of f is a nonempty set of Hausdorff dimension $1$.

Keywords

• Denjoy-Clarkson
• property
• respect
• Hausdorff
• measures
• gradient
• mapping
• functions
• several
• variables