Inequalities and separation for the Laplace–Beltrami differential operator in Hilbert spaces

Zayed, Elsayed M.E.; Mohamed, Adel S.; Atia, H.A.

doi:10.1016/j.jmaa.2006.07.031

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Main Results Definition 31 the Biharmonic Laplace-beltrami1

Introduction1

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2008

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Cited by 8 publications

(3 citation statements)

References 10 publications

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“…Hence, the proof of Theorem 3.1 is completed. 20) and Proof. First, we prove that the homogeneous biharmonic Laplace-Beltrami differential equation…”

Section: Main Results Definition 31 the Biharmonic Laplace-beltramimentioning

confidence: 99%

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

Zayed¹

2016

JPDE

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“…Hence, the proof of Theorem 3.1 is completed. 20) and Proof. First, we prove that the homogeneous biharmonic Laplace-Beltrami differential equation…”

Section: Main Results Definition 31 the Biharmonic Laplace-beltramimentioning

confidence: 99%

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

Zayed¹

2016

JPDE

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“…Recently, Zayed et al [19] have studied the separation for the Laplace Beltrami differential operator in Hilbert spaces and obtained recent results on it.…”

Section: Introductionmentioning

confidence: 99%

Separation for the biharmonic differential operator in the Hilbert space associated with the existence and uniqueness theorem

Zayed

2008

Journal of Mathematical Analysis and Applications

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In this paper, we have studied the separation for the following biharmonic differential operator:is the space of all bounded linear operators on the Hilbert space H 1 and u is the biharmonic differential operator, while u = n i=1 ∂ 2 u ∂x 2 i is the Laplace operator in R n . Moreover, we have studied the existence and uniqueness of the solution of the biharmonic differential equationin the Hilbert space H , where f (x) ∈ H .

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“…Zayed et al [16] have studied the separation of the Laplace-Beltrami differential operator of the form…”

mentioning

confidence: 99%

Separation of bi-harmonic differential operators on Riemannian manifolds

2013

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Consider the bi-harmonic differential expression of the form A D 44 C q on a complete Riemannian manifold .M; g/ with metric g; where 4 is the Laplacian on M and q 0 is a locally square integrable function on M . In the terminology of Everitt and Giertz, the differential expression A is said to be separated in L 2 .M / if for all u 2 L 2 .M / such that Au 2 L 2 .M /, we have qu 2 L 2 .M /. In this paper we give sufficient conditions for A to be separated in L 2 .M /.

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Inequalities and separation for the Laplace–Beltrami differential operator in Hilbert spaces

Abstract: In this paper we have studied the separation for the Laplace-Beltrami differential operator of the form

Cited by 8 publications

References 10 publications

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem

Separation for the biharmonic differential operator in the Hilbert space associated with the existence and uniqueness theorem

Separation of bi-harmonic differential operators on Riemannian manifolds

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