Solvability of a boundary value problem for a second order elliptic differential-operator equation with a complex parameter

Bahram A. Aliev; Vugar Z. Kerimov; Yakov S. Yakubov

doi:10.30546/2409-4994.47.2.309

Solvability of a boundary value problem for a second order elliptic differential-operator equation with a complex parameter

Bahram A. Aliev, Vugar Z. Kerimov, Yakov S. Yakubov

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In a separable Hilbert space H, we study solvability of a boundary value problem for a second order elliptic differential-operator equation with a complex parameter. The parameter enters into the equation and boundary conditions. In addition to the complex parameter, the boundary conditions contain linear operators as well, one of which is unbounded. Application of the obtained abstract results to elliptic boundary value problems is given.

Original language	English
Pages (from-to)	309-326
Number of pages	18
Journal	Proceedings of the Institute of Mathematics and Mechanics
Volume	47
Issue number	2
DOIs	https://doi.org/10.30546/2409-4994.47.2.309
State	Published - 2021

Keywords

Differential-operator equation
Elliptic equation
Fourier transform
Hilbert space
Interpolation spaces
Isomorphism

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10.30546/2409-4994.47.2.309

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abstract = "In a separable Hilbert space H, we study solvability of a boundary value problem for a second order elliptic differential-operator equation with a complex parameter. The parameter enters into the equation and boundary conditions. In addition to the complex parameter, the boundary conditions contain linear operators as well, one of which is unbounded. Application of the obtained abstract results to elliptic boundary value problems is given.",

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AB - In a separable Hilbert space H, we study solvability of a boundary value problem for a second order elliptic differential-operator equation with a complex parameter. The parameter enters into the equation and boundary conditions. In addition to the complex parameter, the boundary conditions contain linear operators as well, one of which is unbounded. Application of the obtained abstract results to elliptic boundary value problems is given.

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KW - Elliptic equation

KW - Fourier transform

KW - Hilbert space

KW - Interpolation spaces

KW - Isomorphism

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Solvability of a boundary value problem for a second order elliptic differential-operator equation with a complex parameter

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