On regularization of the Cauchy problem for elliptic systems in weighted Sobolev spaces : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2019

Идентификатор DOI: 10.1515/jiip-2018-0010

Ключевые слова: The Cauchy problem, ill-posed problems, elliptic operators, Green's formulas, weighted Sobolev spaces

Аннотация: We consider the ill-posed Cauchy problem in a bounded domain To of R-n for an elliptic differential operator A(x, partial derivative) with data on a relatively open subset S of the boundary partial derivative D. We do it in weighted Sobolev spaces H-s,H- gamma(1)) containing the elements with prescribed smoothness s is an element oПоказать полностьюf N and growth near partial derivative S in D, controlled by a real number gamma. More precisely, using proper (left) fundamental solutions of A(x, partial derivative), we obtain a Green-type integral formula for functions from H-s,H- gamma(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 H-s,H- gamma(D) whenever this solution exists.

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Издание

Журнал: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS

Выпуск журнала: Vol. 27, Is. 6

Номера страниц: 815-834

ISSN журнала: 09280219

Место издания: BERLIN

Издатель: WALTER DE GRUYTER GMBH

Авторы

  • Shefer Yulia (Siberian Fed Univ, Inst Math & Comp Sci, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia)
  • Shlapunov Alexander (Siberian Fed Univ, Inst Math & Comp Sci, Pr Svobodnyi 79, Krasnoyarsk 660041, Russia)

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