Fold-Completeness of Generalized Eigenvectors of a Class of Elliptic Problems

Aibeche, Aissa

doi:10.1007/bf03322064

Cited by 3 publications

(1 citation statement)

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“…Boundary value problems for elliptic differential-operator equations were considered in monographs by Krein [16], Dezin [10], Gorbachuk and Gorbachuk [15], Yakubov [23,24], Yakubov and Yakubov [27], Shklyar [20] and in many papers, for example, by Amann [5], deLaubenfels [8], Aibeche [1,2], Yakubov and Aliev [26], Dore and Yakubov [11], Yakubov [25], Aliev and Yakubov [4] and others. All these studies, usually, treat problems in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Second Order Elliptic Differential-Operator Equations with Unbounded Operator Boundary Conditions in UMD Banach Spaces

Aliev

Yakubov

2010

Integr. Equ. Oper. Theory

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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 nonsmooth domains are given.Mathematics Subject Classification (2010). Primary 47E05; Secondary 47A75, 34L10, 34B05, 35P10, 35J25.

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