Sevost’yanov, Е. А. and Salіmov, R. R. and Lomaкo, Тatyana
(2010)
On equicontinuity of solutions to the Beltrami
equations.
Annals of the University of Bucharest (2).
pp. 263274.
Abstract
It is shown that each homeomorphic W1;1
loc solution to the
Beltrami equation @f = � @f is the socalled 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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