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

Abstract Consider the bi-harmonic differential expression of the form A=△M2+q $ A=\triangle _{M}^{2}+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 differe...

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Main Author:	H. A. Atia
Format:	Article
Language:	English
Published:	SpringerOpen 2019-08-01
Series:	Journal of the Egyptian Mathematical Society
Subjects:	Separation problem Bi-harmonic differential operator Manifold
Online Access:	http://link.springer.com/article/10.1186/s42787-019-0029-6

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spelling	doaj-7fb7ccd7839e4fe09e46d799fba9cc2f2020-11-25T03:24:23ZengSpringerOpenJournal of the Egyptian Mathematical Society2090-91282019-08-0127111010.1186/s42787-019-0029-6Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on ManifoldsH. A. Atia0Faculty of Science, Department of Mathematics, Zagazig UniversityAbstract Consider the bi-harmonic differential expression of the form A=△M2+q $ A=\triangle _{M}^{2}+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 L p (M), if for all u∈L p (M) such that Au∈L p (M), we have qu∈L p (M). In this paper, we give sufficient conditions for A to be separated in L p (M),where 1<p<∞.http://link.springer.com/article/10.1186/s42787-019-0029-6Separation problemBi-harmonic differential operatorManifold
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	H. A. Atia
spellingShingle	H. A. Atia Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on Manifolds Journal of the Egyptian Mathematical Society Separation problem Bi-harmonic differential operator Manifold
author_facet	H. A. Atia
author_sort	H. A. Atia
title	Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on Manifolds
title_short	Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on Manifolds
title_full	Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on Manifolds
title_fullStr	Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on Manifolds
title_full_unstemmed	Separation Problem for Bi-Harmonic Differential Operators in L p − spaces on Manifolds
title_sort	separation problem for bi-harmonic differential operators in l p − spaces on manifolds
publisher	SpringerOpen
series	Journal of the Egyptian Mathematical Society
issn	2090-9128
publishDate	2019-08-01
description	Abstract Consider the bi-harmonic differential expression of the form A=△M2+q $ A=\triangle _{M}^{2}+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 L p (M), if for all u∈L p (M) such that Au∈L p (M), we have qu∈L p (M). In this paper, we give sufficient conditions for A to be separated in L p (M),where 1<p<∞.
topic	Separation problem Bi-harmonic differential operator Manifold
url	http://link.springer.com/article/10.1186/s42787-019-0029-6
work_keys_str_mv	AT haatia separationproblemforbiharmonicdifferentialoperatorsinlpspacesonmanifolds
_version_	1724601910405627904

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

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