Bernal-González, L.Jimenez Rodriguez, G. A.Muñoz-Fernández, Gustavo A.Seoane-Sepúlveda, Juan B.2023-06-172023-06-1720171139-113810.1007/s13163-016-0218-xhttps://hdl.handle.net/20.500.14352/17654It 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.engjournal articlehttp://link.springer.com/article/10.1007/s13163-016-0218-xhttp://link.springer.com/restricted access517.5Differentiable functionDomain in the planeFree algebraNon-Lipschitz functionFunciones (Matemáticas)1202 Análisis y Análisis Funcional