Toward the theory of the Sobolev classes with critical exponent
DOI:
https://doi.org/10.15407/dopovidi2019.08.003Keywords:
critical exponent, lower and ring Q homeomorphisms, outer and inner dilatations, Sobolev’s classesAbstract
It is established that an arbitrary homeomorphism f in the Sobolev class
W1,n−1loc
with the outer dilatation
K0(x,f)∈Ln−1loc
is the socalled
lower Q - homeomorphism with
Q=K0(x,f)
and the ring Q* homeomorphism with
Q∗=Kn−10(x,f)
. These results make it possible to research the local and boundary behaviors of the
mappings
W1,n−1loc
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