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Non-Lipschitz differentiable functions on slit domains

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Bernal-González, L. and Jimenez Rodriguez, G. A. and Muñoz-Fernández, Gustavo A. and Seoane-Sepúlveda, Juan B. (2017) Non-Lipschitz differentiable functions on slit domains. Revista matemática complutense . pp. 1-11. ISSN 1139-1138 (In Press)

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Official URL: http://link.springer.com/article/10.1007/s13163-016-0218-x


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Abstract

It is proved the existence of large algebraic structures—including large vector subspaces or infinitely generated free algebras—inside the family of non-Lipschitz differentiable real functions with bounded gradient defined on special non-convex plane domains. In particular, this yields that there are many differentiable functions on plane domains that do not satisfy the mean value theorem.


Item Type:Article
Uncontrolled Keywords:Differentiable function; Domain in the plane; Free algebra; Non-Lipschitz function
Subjects:Sciences > Mathematics > Functions
ID Code:41501
Deposited On:27 Feb 2017 11:52
Last Modified:27 Feb 2017 12:14

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