An Estimate for the Measure of the Preimage of a Ball under -Homeomorphisms

Under study are the homeomorphisms between domains in Euclidean space which belong to a Sobolev class whose geometric properties are governed by controlling the behavior of the capacities of condensers in the preimage through the weighted capacity of the condenser in the image. We obtain some estima...

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Bibliographic Details
Published in:Siberian mathematical journal 2024, Vol.65 (6), p.1395-1401
Main Author: Tomilov, A. O.
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Condensers (liquefiers)
Euclidean geometry
Mathematics
Mathematics and Statistics
Topology
Online Access:Get full text
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Summary:Under study are the homeomorphisms between domains in Euclidean space which belong to a Sobolev class whose geometric properties are governed by controlling the behavior of the capacities of condensers in the preimage through the weighted capacity of the condenser in the image. We obtain some estimates for the measure of the preimage of a ball and inspect the asymptotic behavior at a point.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446624060144