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Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
Published online by Cambridge University Press: 20 November 2018
Abstract
We provide a simple example showing that the tangential derivative of a continuous function $\phi $ can vanish everywhere along a curve while the variation of $\phi $ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.
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- Copyright © Canadian Mathematical Society 2011