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On the differentiability class of the admissible square roots of regular nonnegative functions. (English) Zbl 1228.26004
Bove, Antonio (ed.) et al., Phase space analysis of partial differential equations. Basel: Birkhäuser (ISBN 978-0-8176-4511-3/hbk; 978-0-8176-4521-2/ebook). Progress in Nonlinear Differential Equations and Their Applications 69, 45-53 (2006).
Summary: 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.
For the entire collection see [Zbl 1105.35001].

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
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