Every compact convex subset of matrices is the Clarke Jacobian of some Lipschitzian mapping

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19520%2F21%3AA0000188" target="_blank" >RIV/47813059:19520/21:A0000188 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/21:00545836
Result on the web
<a href="https://www.ams.org/journals/proc/2021-149-11/S0002-9939-2021-15571-8/" target="_blank" >https://www.ams.org/journals/proc/2021-149-11/S0002-9939-2021-15571-8/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/15571" target="_blank" >10.1090/proc/15571</a>

Result language
angličtina
Original language name
Every compact convex subset of matrices is the Clarke Jacobian of some Lipschitzian mapping
Original language description
We prove that every non-empty compact convex subset of m×n matrices is the Clarke Jacobian of a Lipschitzian mapping from ℝ^n to ℝ^m. In detail: Let M be any non-empty compact convex subset of ℝ^{m×n}. We construct a Lipschitzian mapping g:ℝ^n→ℝ^m such that its Clarke generalized Jacobian ∂g(0) at the origin is equal to the given set (∂g(0)=M). In other words, every non-empty compact convex subset of m×n matrices is the Clarke Jacobian of some Lipschitzian mapping from ℝ^n to ℝ^m.
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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