Clarke Jacobians, Bouligand Jacobians, and compact connected sets of matrices

0559493 - MÚ 2023 RIV US eng J - Journal Article
Bartl, D. - Fabian, Marián - Kolář, Jan
Clarke Jacobians, Bouligand Jacobians, and compact connected sets of matrices.
Journal of Mathematical Analysis and Applications. Roč. 516, č. 1 (2022), č. článku 126491. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Bouligand Jacobian * Bouligand subdifferential * Clarke Jacobian * compact connected set of matrices
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jmaa.2022.126491

Recent results on Clarke Jacobians obtained by D. Bartl and M. Fabian are extended to Bouligand Jacobians. In particular, we prove that every non-empty compact connected set of matrices can be expressed as the Bouligand Jacobian at the origin of a suitable Lipschitzian mapping which is moreover either countably piecewise affine or C∞-smooth off the origin. Given proofs are simpler and different from the previous ones.
Permanent Link: https://hdl.handle.net/11104/0332772