Author | Шефер, Юлия Львовна | |
Author | Шлапунов, Александр Анатольевич | |
Accessioned Date | 2020-01-20T08:02:33Z | |
Available Date | 2020-01-20T08:02:33Z | |
Issued Date | 2019-06 | |
Bibliographic Citation | 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. | |
ISSN | 09280219 | |
URI (for links/citations) | https://www.degruyter.com/view/j/jiip.ahead-of-print/jiip-2018-0010/jiip-2018-0010.xml | |
URI (for links/citations) | https://elib.sfu-kras.ru/handle/2311/129671 | |
Abstract | 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. | |
Subject | The Cauchy problem | |
Subject | ill-posed problems | |
Subject | elliptic operators | |
Subject | Green’s formulas | |
Subject | weighted Sobolev spaces | |
Title | On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces | |
Type | Journal Article | |
Type | Journal Article Preprint | |
GRNTI | 27.31.17 | |
Update Date | 2020-01-20T08:02:33Z | |
DOI | 10.1515/jiip-2018-0010 | |
Institute | Институт математики и фундаментальной информатики | |
Department | Кафедра теории функций | |
Journal Name | Journal of Inverse and Ill-Posed Problems | |
Journal Quartile in Scopus | Q3 | |
Journal Quartile in Web of Science | Q2 | |