Elliptic differential-operator problems with the spectral parameter in both the equation and boundary conditions and the corresponding abstract parabolic initial boundary value problems

Yakov Yakubov

doi:10.1007/978-3-319-11406-4_20

Elliptic differential-operator problems with the spectral parameter in both the equation and boundary conditions and the corresponding abstract parabolic initial boundary value problems

Yakov Yakubov^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

6 Scopus citations

Abstract

We consider, in UMD Banach spaces, boundary value problems for second order elliptic differential-operator equations with the spectral parameter and boundary conditions containing the parameter in the same order as the equation. An isomorphism and the corresponding estimate of the solution (with respect to the space variable and the parameter) are obtained. Then, an application of the obtained abstract results is given to boundary value problems for second order elliptic differential equations with the parameter in non-smooth domains. Further, the corresponding abstract parabolic initial boundary value problem is treated and an application to initial boundary value problems with time differentiation in boundary conditions is demonstrated.

Original language	English
Title of host publication	Springer INdAM Series
Publisher	Springer International Publishing
Pages	437-471
Number of pages	35
DOIs	https://doi.org/10.1007/978-3-319-11406-4_20
State	Published - 2014

Publication series

Name	Springer INdAM Series
Volume	10
ISSN (Print)	2281-518X
ISSN (Electronic)	2281-5198

Funding

Funders	Funder number
Israel Ministry of Absorption

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10.1007/978-3-319-11406-4_20

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Elliptic differential-operator problems with the spectral parameter in both the equation and boundary conditions and the corresponding abstract parabolic initial boundary value problems. / Yakubov, Yakov.
Springer INdAM Series. Springer International Publishing, 2014. p. 437-471 (Springer INdAM Series; Vol. 10).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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Elliptic differential-operator problems with the spectral parameter in both the equation and boundary conditions and the corresponding abstract parabolic initial boundary value problems

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