eprintid: 14092
rev_number: 13
eprint_status: archive
userid: 3588
dir: disk0/00/01/40/92
datestamp: 2014-11-20 12:20:28
lastmod: 2015-08-15 10:24:40
status_changed: 2014-11-20 12:20:28
type: article
metadata_visibility: show
title: On spatial mappings with integral restrictions on the characteristic
language: english
abstract: For a given domain D � Rn, some families F of mappings f : D ! Rn,
n � 2 are studied; such families are more general than the mappings with bounded
distortion. It is proved that a family is equicontinuous if
R1
�0
d�
�[�−1(�)]
1
n−1
= 1,
where the integral depends on each mapping f 2 F, � is a special function, and
�0 > 0 is fixed. Under similar restrictions, removability results are obtained for
isolated singularities of f. Also, analogs of the well-known Sokhotsky–Weierstrass
and Liouville theorems are proved.
creators_name: Sevost’yanov, Е. А.
ispublished: pub
subjects: QA77
divisions: sch_man
full_text_status: public
date: 2012
publication: Algebra i analiz
volume: 24
number: 1
pagerange: 1-17
refereed: TRUE
citation:   Sevost’yanov, Е. А.  (2012) On spatial mappings with integral restrictions on the characteristic.  Algebra i analiz, 24 (1).  с. 1-17.      
document_url: http://eprints.zu.edu.ua/14092/1/St_Petersburg_Math_J_%28accepted%29.pdf