2017
Том 69
№ 9

All Issues

Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces

Mikhailets V. A., Murach A. A.

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Abstract

We study a regular elliptic boundary-value problem for a homogeneous differential equation in a bounded domain. We prove that the operator of this problem is a Fredholm (Noether) operator in a two-sided improved scale of functional Hilbert spaces. The elements of this scale are Hörmander-Volevich-Paneyakh isotropic spaces. We establish an a priori estimate for a solution and investigate its regularity.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 11, pp 1748-1767.

Citation Example: Mikhailets V. A., Murach A. A. Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces // Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1536–1555.

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