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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| Format: | Article |
| 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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| Summary: | 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. |
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| ISSN: | 2075-1680 |