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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00559493" target="_blank" >RIV/67985840:_____/22:00559493 - isvavai.cz</a>
Alternative codes found
RIV/47813059:19520/22:A0000286
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2022.126491" target="_blank" >https://doi.org/10.1016/j.jmaa.2022.126491</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126491" target="_blank" >10.1016/j.jmaa.2022.126491</a>

Result language
angličtina
Original language name
Clarke Jacobians, Bouligand Jacobians, and compact connected sets of matrices
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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