{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T10:35:46Z","timestamp":1769078146591,"version":"3.49.0"},"reference-count":57,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T00:00:00Z","timestamp":1741219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We extend Clarke\u2019s 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.<\/jats:p>","DOI":"10.3390\/axioms14030195","type":"journal-article","created":{"date-parts":[[2025,3,6]],"date-time":"2025-03-06T04:55:08Z","timestamp":1741236908000},"page":"195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Inverse and Implicit Function Theorem for Sobolev Mappings"],"prefix":"10.3390","volume":"14","author":[{"given":"Mihai","family":"Cristea","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Sciences, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dontchev, A.I., and Rockafellar, R.T. (2014). Implicit Functions and Solution Mappings, Springer. 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