Décomposition polaire et réarrangement monotone des champs de vecteurs. (Polar decomposition and increasing rearrangement of vector fields). (French) Zbl 0652.26017

Under certain hypotheses the author demonstrates that a given vector field \(\phi\) defined on a compact set K of \(R^ d\) can be factorized in the form \(\phi =\nabla u\circ g,\) where u is a convex function defined on K and g is a volume preserving mapping from K into itself.
Reviewer: S.K.Chatterjea


26B99 Functions of several variables