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

PERNAZZA, LUDOVICO;
2006

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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