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


Тип публикации: статья из журнала

Год издания: 2019

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

Аннотация: We consider the ill-posed Cauchy problem in a bounded domain D of R-n for an elliptic differential operator A (x, δ) A (x,) with data on a relatively open subset S of the boundary â â¡ δ D. We do it in weighted Sobolev spaces H s, γ (Δy) {H-s,γ}(D) containing the elements with prescribed smoothness s {s\in\mathbb{N}} and growth neaПоказать полностьюr S S in δ D, controlled by a real number γ. More precisely, using proper (left) fundamental solutions of ¢ (x, -) A, we obtain a Green-type integral formula for functions from H s, γ (δY) {H-s,\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, γ D (δY) {H-s,γ D whenever this solution exists.

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Журнал: Journal of Inverse and Ill-Posed Problems

ISSN журнала: 09280219

Издатель: Brill Academic Publishers


  • Shefer Y. (Institute of Mathematics and Computer Science,Siberian Federal University)
  • Shlapunov A. (Institute of Mathematics and Computer Science,Siberian Federal University)

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