Uniform separable differential operators with parameters

Ravi P. Agarwal; Donal O'Regan; Veli B. Shakhmurov

doi:10.1016/j.jfranklin.2009.06.003

Uniform separable differential operators with parameters

Ravi P. Agarwal
, Donal O'Regan
, Veli B. Shakhmurov

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued L_p-spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters.

Original language	English
Pages (from-to)	2-16
Number of pages	15
Journal	Journal of the Franklin Institute
Volume	347
Issue number	1
DOIs	https://doi.org/10.1016/j.jfranklin.2009.06.003
Publication status	Published - 1 Feb 2010

Keywords

Banach-valued function spaces
Differential equations with parameters
Differential-operator equations
Interpolation of Banach spaces
Operator-valued Fourier multipliers
Semigroups of operators

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Agarwal, RP;O'Regan, D;Shakhmurov, VB

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10.1016/j.jfranklin.2009.06.003

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abstract = "In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued Lp-spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters.",

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T1 - Uniform separable differential operators with parameters

AU - Agarwal, Ravi P.

AU - O'Regan, Donal

AU - Shakhmurov, Veli B.

PY - 2010/2/1

Y1 - 2010/2/1

N2 - In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued Lp-spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters.

AB - In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued Lp-spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters.

KW - Banach-valued function spaces

KW - Differential equations with parameters

KW - Differential-operator equations

KW - Interpolation of Banach spaces

KW - Operator-valued Fourier multipliers

KW - Semigroups of operators

UR - https://www.scopus.com/pages/publications/73649142049

U2 - 10.1016/j.jfranklin.2009.06.003

DO - 10.1016/j.jfranklin.2009.06.003

M3 - Article

SN - 0016-0032

VL - 347

SP - 2

EP - 16

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 1

ER -

Uniform separable differential operators with parameters

Abstract

Keywords

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