A Note on Clarke’s Generalized Jacobian for the Inverse of Bi-Lipschitz Maps

URN to cite this document:: urn:nbn:de:bvb:355-epub-551552
DOI to cite this document:: 10.5283/epub.55155

Behr, Florian ; Dolzmann, Georg

License: Creative Commons Attribution 4.0
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Date of publication of this fulltext: 07 Dec 2023 08:45

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Abstract

Clarke’s inverse function theorem for Lipschitz mappings states that a bi-Lipschitz mapping f is locally invertible about a point x0 if the generalized Jacobian ∂ f (x0) does not contain singular matrices. It is shown that under these assumptions the generalized Jacobian of the inverse mapping at f (x0) is the convex hull of the set of matrices that can be obtained as limits of sequences J f (xk ...