%A ?. ?. Sevost?yanov
%A R. R. Sal?mov
%A ?atyana Loma?o
%J Annals of the University of Bucharest
%T On equicontinuity of solutions to the Beltrami
equations
%X 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.
%N 2
%K Beltrami equations, equicontinuity, normality,
lower and ring Q{homeomorphisms.
%P 263-274
%D 2010
%L zu213947