Abstract
We survey recent results on the structure of the range of the derivative of a smooth mapping between two Banach spaces and . We recall some necessary conditions and some sufficient conditions on a subset of for the existence of a Fréchet differentiable mapping from into so that . Whenever is only assumed Gâteaux differentiable, new phenomena appear: for instance, there exists a mapping from into , which is bounded, Lipschitz-continuous, and so that for all , if , then .
Citation
Robert Deville. "On the range of the derivative of a smooth mapping between Banach spaces." Abstr. Appl. Anal. 2005 (5) 499 - 507, 30 June 2005. https://doi.org/10.1155/AAA.2005.499
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