Библиографическое описание:Shestakov, Ivan. Negative Sobolev Spaces in the Cauchy Problem for the Cauchy-Riemann Operator / I. V. Shestakov, A. A. Shlapunov. - Текст : непосредственный // Журнал Сибирского федерального университета. Математика и физика. - 2009. - Т. 2, № 1. - С. 17-30. - Библиогр.: с. 29-30. - ISSN 1997-1397.
Аннотация: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.
