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Journal of Siberian Federal University. Mathematics & Physics, 2008, Volume 1, Issue 1, Pages 52–62
(Mi jsfu6)
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This article is cited in 2 scientific papers (total in 2 papers)
On the Cauchy Problem for Operators with Injective Symbols in Sobolev Spaces
Ivan V. Shestakov, Alexander A. Shlapunov Institute of Mathematics, Siberian Federal University
Abstract:
Let DD be a bounded domain in Rn (n⩾2) with a smooth boundary ∂D. We describe necessary and sufficient solvability conditions (in Sobolev spaces in D) of the ill-posed non-homogeneous Cauchy problem for a partial differential operator A with injective symbol and of order m⩾1. Moreover, using bases with the double orthogonality property we construct Carleman's formulae for (vector-) functions from the Sobolev space Hs(D), s⩾m, by their Cauchy data on Γ and the values of Au in D where Γ is an open (in the topology of ∂D) connected part of the boundary.
Keywords:
ill-posed Cauchy problem, Carleman's formula, bases with double orthogonality.
Received: 11.10.2007 Received in revised form: 20.11.2007 Accepted: 05.12.2007
Citation:
Ivan V. Shestakov, Alexander A. Shlapunov, “On the Cauchy Problem for Operators with Injective Symbols in Sobolev Spaces”, J. Sib. Fed. Univ. Math. Phys., 1:1 (2008), 52–62
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https://www.mathnet.ru/eng/jsfu6 https://www.mathnet.ru/eng/jsfu/v1/i1/p52
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Abstract page: | 402 | Full-text PDF : | 112 | References: | 66 |
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