Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, \sigma )-weighted (q, p)-distortion on Carnot groups
https://doi.org/10.26907/0021-3446-2024-3-84-90
Abstract
In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.
About the Authors
S. K. Vodopyanov
Novosibirsk State University
Russian Federation
Russian Federation
Sergey Konstantinovich Vodopyanov
1 Pirogova str., Novosibirsk, 630090
D. A. Sboev
Novosibirsk State University
Russian Federation
Russian Federation
Danil Alekseevich Sboev
1 Pirogova str., Novosibirsk, 630090
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Review
For citations:
Vodopyanov S.K., Sboev D.A. Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, \sigma )-weighted (q, p)-distortion on Carnot groups. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(3):84-90. (In Russ.) https://doi.org/10.26907/0021-3446-2024-3-84-90
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