TY - JOUR

T1 - An Estimate for the Measure of the Preimage of a Ball under -Homeomorphisms

AU - Tomilov, A. O.

N1 - The work was supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/11

Y1 - 2024/11

N2 - Under study are the homeomorphisms between domains in Euclidean space which belong to a Sobolevclass whose geometric properties are governed by controlling the behavior of the capacitiesof 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 asymptoticbehavior at a point.

AB - Under study are the homeomorphisms between domains in Euclidean space which belong to a Sobolevclass whose geometric properties are governed by controlling the behavior of the capacitiesof 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 asymptoticbehavior at a point.

KW - 517.518:517.54

KW - Sobolev space

KW - asymptotics at a point

KW - capacity of a condenser

KW - composition operator

KW - measure of a ball

KW - quasiconformal analysis

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85209396247&origin=inward&txGid=8053b134a12074494312a10ce986e47a

UR - https://www.mendeley.com/catalogue/010798ad-2df2-3c6e-8431-0243da597b8b/

U2 - 10.1134/S0037446624060144

DO - 10.1134/S0037446624060144

M3 - Article

VL - 65

SP - 1395

EP - 1401

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -