Sobolev Mappings and Moduli Inequalities on Carnot Groups

Evgenii A. Sevost’yanov; Alexander Ukhlov

doi:10.1007/s10958-020-04971-2

Sobolev Mappings and Moduli Inequalities on Carnot Groups

Evgenii A. Sevost’yanov, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

Abstract. We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities (Q-homeomorphisms) with a locally integrable function Q are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups G; the mappings inverse to Sobolev homeomorphisms of finite distortion of the class Wv,loc1(ΩΩ′) belong to the Sobolev class W1,loc1(Ω′Ω).

Original language	American English
Pages (from-to)	754-768
Number of pages	15
Journal	Journal of Mathematical Sciences
Volume	249
Issue number	5
DOIs	https://doi.org/10.1007/s10958-020-04971-2
State	Published - 1 Sep 2020

Keywords

Carnot group
Sobolev spaces
moduli inequalities

All Science Journal Classification (ASJC) codes

Applied Mathematics
Statistics and Probability
General Mathematics

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10.1007/s10958-020-04971-2

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abstract = "Abstract. We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities (Q-homeomorphisms) with a locally integrable function Q are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups G; the mappings inverse to Sobolev homeomorphisms of finite distortion of the class Wv,loc1(ΩΩ′) belong to the Sobolev class W1,loc1(Ω′Ω).",

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AU - Ukhlov, Alexander

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N2 - Abstract. We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities (Q-homeomorphisms) with a locally integrable function Q are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups G; the mappings inverse to Sobolev homeomorphisms of finite distortion of the class Wv,loc1(ΩΩ′) belong to the Sobolev class W1,loc1(Ω′Ω).

AB - Abstract. We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities (Q-homeomorphisms) with a locally integrable function Q are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups G; the mappings inverse to Sobolev homeomorphisms of finite distortion of the class Wv,loc1(ΩΩ′) belong to the Sobolev class W1,loc1(Ω′Ω).

KW - Carnot group

KW - Sobolev spaces

KW - moduli inequalities

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U2 - 10.1007/s10958-020-04971-2

DO - 10.1007/s10958-020-04971-2

M3 - Article

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VL - 249

SP - 754

EP - 768

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

IS - 5

ER -

Sobolev Mappings and Moduli Inequalities on Carnot Groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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