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.
CITATION STYLE
Bernal-González, L., Jiménez-Rodríguez, P., Muñoz-Fernández, G. A., & Seoane-Sepúlveda, J. B. (2017). Non-Lipschitz differentiable functions on slit domains. Revista Matematica Complutense, 30(2), 269–279. https://doi.org/10.1007/s13163-016-0218-x
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