Separation Problem for Bi-Harmonic Differential Operators in Lp− spaces on Manifolds - Egyptian Knowledge Bank

383454

Separation Problem for Bi-Harmonic Differential Operators in Lp− spaces on Manifolds

Article

Last updated: 05 Jan 2025

Subjects

Abstract

Consider the bi-harmonic differential expression of the form
A = 2M² + q
on a manifold of bounded geometry (M, g) with metric g, where M is the scalar
Laplacian on M and q ≥ 0 is a locally integrable function on M.
In the terminology of Everitt and Giertz, the differential expression A is said to be
separated in Lp (M), if for all u ∈ Lp (M) such that Au ∈ Lp (M), we have qu ∈ Lp (M). In
this paper, we give sufficient conditions for A to be separated in Lp (M),where
1 < p < ∞

DOI

10.1186/s42787-019-0029-6

Keywords

Separation problem, Bi-harmonic differential operator, Manifold

Authors

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First Name

Last Name

Atia

MiddleName

Affiliation

Faculty of Science, Department of Mathematics, Zagazig University, Zagazig, Egypt

Email

City

Orcid

Volume

Article Issue

Related Issue

50652

Issue Date

2019-12-01

Receive Date

2024-10-02

Publish Date

2019-12-01

Page Start

Page End

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 27_Issue 1_Pages 1-10.pdf

PDF . 444.3kB

Link

https://joems.journals.ekb.eg/article_383454.html

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https://joems.journals.ekb.eg/service?article_code=383454

Order

383,454

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

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