Ukrainian Mathematical Bulletin

Volume 3, Issue 4, 2006 pp. 529-560.

Elliptic Operator with Homogeneous Regular Boundary Conditions in a Two-side Refined Scale of Spaces

Authors: Vladimir Andreevich Mikhailets, Aleksandr Aleksandrovich Murach
Author institution: Institute of Mathematics of the National Academy of Sciences of Ukraine, 3, ul. Tereshchenkovskaya, 01601, Kiev--4, Ukraine, mikhailets@imath.kiev.ua, murach@imath.kiev.ua

Summary: We study a regular elliptic boundary-value problem with homogeneous boundary conditions on a bounded region in the space $\mathbb{R}^{n}$. It is proved that the operator of such a problem has finite index and gives rise to a family of isomorphisms in a two-side refined scale of function Hilbert spaces. Elements of this scale are isotropic H\"ormander--Volevich--Paneyakh spaces. An a priori estimate for the solution of the problem is established.

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