Sobolev mappings and moduli inequalities on Carnot groups-Reference-Cited by-同舟云学术

Sobolev mappings and moduli inequalities on Carnot groups

Published:2020-06-22 Issue:2 Volume:17 Page:215-233
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Sevost'yanov Evgenii¹,Ukhlov Alexander²

Affiliation:

1. I. Franko Zhytomyr State University, Zhytomyr, Ukraine, Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Slavyansk, Ukraine

2. Department of Mathematics, Ben-Gurion University of the Negev, Beer Sheva, Israel

Abstract

We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities ($Q$-homeomor\-phisms) 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 $\mathbb G,$ the mappings inverse to Sobolev homeomorphisms of finite distortion of the class $W^1_{\nu,\loc}(\Omega;\Omega')$ belong to the Sobolev class $W^1_{1,\loc}(\Omega';\Omega)$.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

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