We investigate the possibility of writing $f = g^2$ when $f$ is a $C^k$ nonnegative function with $k \geq 6$. We prove that, assuming that $f$ vanishes at all its local minima, it is possible to get $g \in C^2$ and three times differentiable at every point, but that one cannot ensure any additional regularity.

On the differentiability class of the admissible square roots of regular nonnegative functions

Abstract

We investigate the possibility of writing $f = g^2$ when $f$ is a $C^k$ nonnegative function with $k \geq 6$. We prove that, assuming that $f$ vanishes at all its local minima, it is possible to get $g \in C^2$ and three times differentiable at every point, but that one cannot ensure any additional regularity.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/27301
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