On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces
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Автор:
Шефер, Юлия Львовна
Шлапунов, Александр Анатольевич
Коллективный автор:
Институт математики и фундаментальной информатики
Кафедра теории функций
Дата:
2019-06Журнал:
Journal of Inverse and Ill-Posed ProblemsКвартиль журнала в Scopus:
Q3Квартиль журнала в Web of Science:
Q2Библиографическое описание:
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.Аннотация:
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.
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