2019
Том 71
№ 9

All Issues

On the Sobolev problem in the complete scale of Banach spaces

Los’ V. M., Roitberg Ya. A.

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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.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 9, pp 1330-1342.

Citation Example: Los’ V. M., Roitberg Ya. A. On the Sobolev problem in the complete scale of Banach spaces // Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1181–1192.

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