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).
pp. 263-274.
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.
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