N. A. Kudryavtseva, S. K. Vodopyanov, “On the convergence of mappings with <nobr>$k$</nobr>-finite distortion”, Probl. Anal. Issues Anal., 2018, Volume 7(25), special issue,Pages <nobr>88

On the convergence of mappings with $k$-finite distortion

N. A. Kudryavtseva^a, S. K. Vodopyanov^b

^a Novosibirsk State University, 1 Pirogova str., Novosibirsk 630090, Russia
^b Sobolev Institute of Mathematics, 4 Akademika Koptyuga pr., Novosibirsk 630090, Russia

Abstract: We prove that a locally uniform limit of a sequence of homeomorphisms with finite $k$-distortion is also a mapping with finite $k$-distortion. We obtain also an estimation for the distortion coefficient of the limit mapping.

Keywords: mapping with $k$-finite distortion, distortion coefficient, passing to the limit, differential form.

UDC: 517.518

MSC: 30C65

Received: 31.05.2018
Revised: 18.06.2018
Accepted: 18.09.2018

Language: English

DOI: 10.15393/j3.art.2018.5511