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On the Sobolev problem in the complete scale of Banach spaces

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Abstract

In a bounded domainG with boundary ∂G that consists of components of different dimensions, we consider an elliptic boundary-value problem in complete scales of Banach spaces. The orders of boundary expressions are arbitrary; they are pseudodifferential along ∂G. We prove the theorem on a complete set of isomorphisms and generalize its application. The results obtained are true for elliptic Sobolev problems with a parameter and parabolic Sobolev problems as well as for systems with the Douglis-Nirenberg structure.

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Chernigov Pedagogical Institute, Chernigov. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1181–1192, September, 1999.

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Los', V.N., Roitberg, Y.A. On the Sobolev problem in the complete scale of Banach spaces. Ukr Math J 51, 1330–1342 (1999). https://doi.org/10.1007/BF02593000

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  • DOI: https://doi.org/10.1007/BF02593000

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