Библиографическое описание:Shestakov, I. V. On the Cauchy Problem for Operators with Injective Symbols in Sobolev Spaces / I. V. Shestakov, A. A. Shlapunov. - Текст : непосредственный // Журнал Сибирского федерального университета. Математика и физика. - 2008. - Т. 1, № 1. - С. 52-62. - Библиогр.: с. 61-62 (18 назв.). - ISSN 1997-1397.
Аннотация:Let D be a bounded domain in R n (n more or equal 2) with a smooth boundary private differential D. We describe necessary and sufficient solvability conditions (in Sobolev spaces in D) of the ill-posed non-homogeneous Cauchy problem for a partial differential operator A with injective symbol and of order m more or equal 1. Moreover, using bases with the double orthogonality property we construct Carleman’s formulae for (vector-) functions from the Sobolev space Hs (D), s more or equal m, by their Cauchy data on Г and the values of Au in D where Г is an open (in the topology of private differential D) connected part of the boundary.
