Negative Sobolev Spaces in the Cauchy Problem for the Cauchy-Riemann Operator
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https://elib.sfu-kras.ru/handle/2311/877Author:
Shestakov, Ivan V.
Shlapunov, Alexander A.
(Ivan V.Shestakov: Institute of Mathematics
Siberian Federal University,
av. Svobodny 79, Krasnoyarsk, 660041,
Russia, e-mail: Shestakov-V@yandex.ru; Alexander A.Shlapunov: Institute of Mathematics
Siberian Federal University,
av. Svobodny 79, Krasnoyarsk, 660041,
Russia, e-mail: shlapuno@lan.krasu.ru)
Date:
2009-01Abstract:
Let D be a bounded domain in Cn (n > 1) with a smooth boundary @D. We indicate appropriate Sobolev
spaces of negative smoothness to study the non-homogeneous Cauchy problem for the Cauchy-Riemann
operator @ in D. In particular, we describe traces of the corresponding Sobolev functions on @D and give
an adequate formulation of the problem. Then we prove the uniqueness theorem for the problem, describe
its necessary and sufficient solvability conditions and produce a formula for its exact solution.
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