Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space
- Autores: Menovshchikov A.1,2
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Afiliações:
- Sobolev Institute of Mathematics Novosibirsk State University
- Peoples’ Friendship University of Russia
- Edição: Volume 58, Nº 4 (2017)
- Páginas: 649-662
- Seção: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171327
- DOI: https://doi.org/10.1134/S0037446617040115
- ID: 171327
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Resumo
Given a homeomorphism ϕ ∈ WM1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF1. We also obtain necessary and sufficient conditions under which a homeomorphism of domains in a Euclidean space induces the bounded composition operator of Sobolev–Orlicz spaces defined by a special class of N-functions. Using these results, we establish requirements on a mapping under which the inverse homeomorphism also induces the bounded composition operator of another pair of Sobolev–Orlicz spaces which is defined by the first pair.
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Sobre autores
A. Menovshchikov
Sobolev Institute of Mathematics Novosibirsk State University; Peoples’ Friendship University of Russia
Autor responsável pela correspondência
Email: antikoerper@mail.ru
Rússia, Novosibirsk; Moscow