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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| Language: | English |
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MDPI AG
2025-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/14/3/195 |
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| _version_ | 1850205534511169536 |
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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 |
| id | doaj-art-26fa3a90628c4c2cb147210fa3371c6d |
| 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 |