On Inverse and Implicit Function Theorem for Sobolev Mappings

We extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second variable. An application to control systems is give...

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Main Author: Mihai Cristea
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/3/195
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author Mihai Cristea
author_facet Mihai Cristea
author_sort Mihai Cristea
collection DOAJ
description We extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second variable. An application to control systems is given.
format Article
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institution OA Journals
issn 2075-1680
language English
publishDate 2025-03-01
publisher MDPI AG
record_format Article
series Axioms
spelling doaj-art-26fa3a90628c4c2cb147210fa3371c6d2025-08-20T02:11:04ZengMDPI AGAxioms2075-16802025-03-0114319510.3390/axioms14030195On Inverse and Implicit Function Theorem for Sobolev MappingsMihai Cristea0Faculty of Mathematics and Computer Sciences, University of Bucharest, Str. Academiei 14, 010014 Bucharest, RomaniaWe extend Clarke’s local inversion theorem for Sobolev mappings. We use this result to find a general implicit function theorem for continuous locally Lipschitz mapping in the first variable and satisfying just a topological condition in the second variable. An application to control systems is given.https://www.mdpi.com/2075-1680/14/3/195local and global univalenceimplicit function theoremSobolev mappings
spellingShingle Mihai Cristea
On Inverse and Implicit Function Theorem for Sobolev Mappings
Axioms
local and global univalence
implicit function theorem
Sobolev mappings
title On Inverse and Implicit Function Theorem for Sobolev Mappings
title_full On Inverse and Implicit Function Theorem for Sobolev Mappings
title_fullStr On Inverse and Implicit Function Theorem for Sobolev Mappings
title_full_unstemmed On Inverse and Implicit Function Theorem for Sobolev Mappings
title_short On Inverse and Implicit Function Theorem for Sobolev Mappings
title_sort on inverse and implicit function theorem for sobolev mappings
topic local and global univalence
implicit function theorem
Sobolev mappings
url https://www.mdpi.com/2075-1680/14/3/195
work_keys_str_mv AT mihaicristea oninverseandimplicitfunctiontheoremforsobolevmappings