Second Order Elliptic Differential-Operator Equations with Unbounded Operator Boundary Conditions in <Emphasis Type="Italic">UMD</Emphasis> Banach Spaces |
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Authors: | B?A?Aliev Email author" target="_blank">Ya?YakubovEmail author |
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Institution: | 1.National Academy of Sciences of Azerbaijan,Institute of Mathematics and Mechanics,Baku,Azerbaijan Republic;2.Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences,Tel-Aviv University,Ramat-Aviv,Israel |
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Abstract: | In a UMD Banach space E, we consider a boundary value problem for a second order elliptic differential-operator equation with a spectral parameter
when one of the boundary conditions, in the principal part, contains a linear unbounded operator in E. A theorem on an isomorphism is proved and an appropriate estimate of the solution with respect to the space variable and
the spectral parameter is obtained. In this way, Fredholm property of the problem is shown. Moreover, discreteness of the
spectrum and completeness of a system of root functions corresponding to the homogeneous problem are established. Finally,
applications of obtained abstract results to nonlocal boundary value problems for elliptic differential equations with a parameter
in non-smooth domains are given. |
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Keywords: | |
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