Zhuravlev I.V. An inplicit function theorem for sobolev mappings

http://dx.doi.org/10.15688/jvolsu1.2012.2.3

Zhuravlev Igor Vladimirovich
 
Doctor of Physics and Mathematics, Professor, Chair of Mathematical Analysis and Function Theory, Volgograd State University
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Prospect Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. In the paper we obtained a nonsmooth version of the implicit function theorem. We proved the implicit function theorem for mappings with Sobolev’s derivatives. Our method of proof uses a normalized Jacobi matrix.

Key words: implicit functions, normalized Jacobi matrix, Clarke derivative, inverse function, Sobolev’s derivatives.

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An implicit function theorem for Sobolev mappings by Zhuravlev I.V. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (17) 2012 pp. 13-17

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