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Шефер, Юлия Львовна
Шлапунов, Александр Анатольевич
2020-01-20T08:02:33Z
2020-01-20T08:02:33Z
2019-06
Шефер, Юлия Львовна. On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces [Текст] / Юлия Львовна Шефер, Александр Анатольевич Шлапунов // Journal of Inverse and Ill-Posed Problems. — 2019.
09280219
https://www.degruyter.com/view/j/jiip.ahead-of-print/jiip-2018-0010/jiip-2018-0010.xml
https://elib.sfu-kras.ru/handle/2311/129671
We consider the ill-posed Cauchy problem in a bounded domain D of Rn for an elliptic differential operator A(x,∂) with data on a relatively open subset S of the boundary ∂D. We do it in weighted Sobolev spaces Hs,γ(D) containing the elements with prescribed smoothness s∈N and growth near ∂S in D, controlled by a real number γ. More precisely, using proper (left) fundamental solutions of A(x,∂), we obtain a Green-type integral formula for functions from Hs,γ(D). Then a Neumann-type series, constructed with the use of iterations of the (bounded) integral operators applied to the data, gives a solution to the Cauchy problem in Hs,γ(D) whenever this solution exists.
The Cauchy problem
ill-posed problems
elliptic operators
Green’s formulas
weighted Sobolev spaces
On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces
Journal Article
Journal Article Preprint
27.31.17
2020-01-20T08:02:33Z
10.1515/jiip-2018-0010
Институт математики и фундаментальной информатики
Кафедра теории функций
Journal of Inverse and Ill-Posed Problems
Q3
Q2


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