Differential and Integral Equations

Completeness of root vectors for an Agmon-Douglis-Nirenberg elliptic problem with an indefinite weight in $L_p$ spaces

Mamadou Sango

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This paper is devoted to the systematic investigation of the completeness of root vectors (generalized eigenvectors) of a non-selfadjoint Agmon-Douglis-Nirenberg (ADN) elliptic boundary problem with an indefinite weight matrix. As it is known the realization of a ADN elliptic problem (or simply a correctly posed general elliptic boundary problem in which no restrictions are imposed on the order of some boundary operators) is not in general densely defined. This amounts to some tremendous difficulties in the derivation of the completeness of the root vectors for the corresponding spectral problem. However under some circumstances the completeness of root vectors may be obtained in some dense subsets of functions in Sobolev spaces. These issues are addressed in the present work for a class of non-selfadjoint ADN elliptic boundary value problems with an indefinite weight matrix-function for which we establish new completeness results for the corresponding root vectors in appropriate $L_{p}$ Sobolev spaces.

Article information

Differential Integral Equations, Volume 15, Number 10 (2002), 1237-1262.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35P10: Completeness of eigenfunctions, eigenfunction expansions
Secondary: 35J55 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)


Sango, Mamadou. Completeness of root vectors for an Agmon-Douglis-Nirenberg elliptic problem with an indefinite weight in $L_p$ spaces. Differential Integral Equations 15 (2002), no. 10, 1237--1262. https://projecteuclid.org/euclid.die/1356060753

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