Publication: Non-Lipschitz differentiable functions on slit domains
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Publication Date
2017
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Springer
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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.