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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 11, pp. 1536–1555, November, 2006.
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Mikhailets, V.A., Murach, A.A. Regular elliptic boundary-value problem for a homogeneous equation in a two-sided improved scale of spaces. Ukr Math J 58, 1748–1767 (2006). https://doi.org/10.1007/s11253-006-0166-6
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DOI: https://doi.org/10.1007/s11253-006-0166-6