Regularity of the inverse of a homeomorphism of a Sobolev

Standard

Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space. / Menovshchikov, A. V.

In: Siberian Mathematical Journal, Vol. 58, No. 4, 01.07.2017, p. 649-662.

Research output: Contribution to journal › Article › peer-review

Harvard

Menovshchikov, AV 2017, 'Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space', Siberian Mathematical Journal, vol. 58, no. 4, pp. 649-662. https://doi.org/10.1134/S0037446617040115

APA

Menovshchikov, A. V. (2017). Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space. Siberian Mathematical Journal, 58(4), 649-662. https://doi.org/10.1134/S0037446617040115

Vancouver

Menovshchikov AV. Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space. Siberian Mathematical Journal. 2017 Jul 1;58(4):649-662. doi: 10.1134/S0037446617040115

Author

Menovshchikov, A. V. / Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space. In: Siberian Mathematical Journal. 2017 ; Vol. 58, No. 4. pp. 649-662.

BibTeX

@article{08944a544e214993aaf8a2de8ba893c7,

title = "Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space",

abstract = "Given a homeomorphism ϕ ∈ WM 1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF 1. 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.",

keywords = "codistortion, composition operator, distortion, N-function, Sobolev–Orlicz space, FINITE DISTORTION, Sobolev-Orlicz space, DERIVATIVES, OPERATORS, QUASICONFORMAL MAPPINGS, EXTREMAL MAPPINGS",

author = "Menovshchikov, {A. V.}",

note = "Publisher Copyright: {\textcopyright} 2017, Pleiades Publishing, Ltd.",

year = "2017",

month = jul,

day = "1",

doi = "10.1134/S0037446617040115",

language = "English",

volume = "58",

pages = "649--662",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "4",

}

RIS

TY - JOUR

T1 - Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space

AU - Menovshchikov, A. V.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Given a homeomorphism ϕ ∈ WM 1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF 1. 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.

AB - Given a homeomorphism ϕ ∈ WM 1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF 1. 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.

KW - codistortion

KW - composition operator

KW - distortion

KW - N-function

KW - Sobolev–Orlicz space

KW - FINITE DISTORTION

KW - Sobolev-Orlicz space

KW - DERIVATIVES

KW - OPERATORS

KW - QUASICONFORMAL MAPPINGS

KW - EXTREMAL MAPPINGS

UR - http://www.scopus.com/inward/record.url?scp=85028527327&partnerID=8YFLogxK

U2 - 10.1134/S0037446617040115

DO - 10.1134/S0037446617040115

M3 - Article

AN - SCOPUS:85028527327

VL - 58

SP - 649

EP - 662

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 9918465