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.File in questo prodotto:
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