Abstract
We investigate the possibility of writing f = g 2 when f is a C k nonnegative function with k ≥ 6. We prove that, assuming that f vanishes at all its local minima, it is possible to get g ∈ C 2 and three times differentiable at every point, but that one cannot ensure any additional regularity.
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© 2006 Birkhäuser Boston
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Bony, JM., Colombini, F., Pernazza, L. (2006). On the differentiability class of the admissible square roots of regular nonnegative functions. In: Bove, A., Colombini, F., Del Santo, D. (eds) Phase Space Analysis of Partial Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 69. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4521-2_4
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DOI: https://doi.org/10.1007/978-0-8176-4521-2_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4511-3
Online ISBN: 978-0-8176-4521-2
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