eprintid: 13947
rev_number: 12
eprint_status: archive
userid: 3588
dir: disk0/00/01/39/47
datestamp: 2014-11-12 10:01:16
lastmod: 2015-08-15 10:12:00
status_changed: 2014-11-12 10:01:16
type: article
metadata_visibility: show
title: On equicontinuity of solutions to the Beltrami
equations
language: english
abstract: It is shown that each homeomorphic W1;1
loc solution to the
Beltrami equation @f = � @f is the so-called ring Q{homeomorphism with
Q(z) = K�(z) where K�(z) is the dilatation quotient of this equation. On
this base, it is stated equicontinuity and normality of families of such solu-
tions under the conditions that K�(z) has a majorant of �nite mean oscil-
lRation, singularities of logarithmic type or integral constraints of the type
�(K�(z)) dx dy < 1 in a domain D � C: The found conditions on the
function � are not only su�cient but also necessary for equicontinuity and
normality of the corresponding families of solutions to the Beltrami equa-
tion.
keywords: Beltrami equations, equicontinuity, normality,
lower and ring Q{homeomorphisms.
creators_name: Sevost’yanov, Е. А.
creators_name: Salіmov, R. R.
creators_name: Lomaкo, Тatyana
ispublished: pub
subjects: QA77
divisions: sch_man
full_text_status: public
date: 2010
publication: Annals of the University of Bucharest
number: 2
pagerange: 263-274
refereed: TRUE
citation:   Sevost’yanov, Е. А., Salіmov, R. R., Lomaкo, Тatyana  (2010) On equicontinuity of solutions to the Beltrami equations.  Annals of the University of Bucharest (2).  с. 263-274.      
document_url: http://eprints.zu.edu.ua/13947/1/lomako_etal.pdf