最終更新日:2022/12/24
We then use a limiting Cauchy integral along level curves of Green's function to show that the Plemelj-Sokhotski jump formula holds on quasicircles with boundary data in the Douglas-Osborn space, which also enable us to prove the well-posedness of a Riemann-Hilbert problem with boundary data in Douglas-Osborn space on quasicircles.
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We
then
use
a
limiting
Cauchy
integral
along
level
curves
of
Green's
function
to
show
that
the
Plemelj-Sokhotski
jump
formula
holds
on
quasicircles
with
boundary
data
in
the
Douglas-Osborn
space,
which
also
enable
us
to
prove
the
well-posedness
of
a
Riemann-Hilbert
problem
with
boundary
data
in
Douglas-Osborn
space
on
quasicircles.