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Separation of bi-harmonic differential operators on Riemannian manifolds

  • Hany A. Atia EMAIL logo , Ramzi S. Alsaedi und Ahmed Ramady
Veröffentlicht/Copyright: 1. November 2013
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 26 Heft 3

Abstract.

Consider the bi-harmonic differential expression of the form A=▵▵+q on a complete Riemannian manifold (M,g) with metric g, where ▵ 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 L2(M) if for all u∈L2(M) such that Au∈L2(M), we have qu∈L2(M). In this paper we give sufficient conditions for A to be separated in L2(M).

Keywords: Separation; bi-harmonic differential operator; Riemannian manifolds
MSC: 47F05; 58J99

Funding source: Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah

Award Identifier / Grant number: 285/662/1431

Received: 2013-7-30
Published Online: 2013-11-1
Published in Print: 2014-5-1

© 2014 by Walter de Gruyter Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Smooth global solutions for the two-dimensional Euler Poisson system
  3. Primitive ideals in quantum Schubert cells: Dimension of the strata
  4. Group valued null sequences and metrizable non-Mackey groups
  5. The splitting relation for Fréchet spaces over non-archimedean fields
  6. Bloch–Kato pro-p groups and locally powerful groups
  7. On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds
  8. The Ext functor and self-sums
  9. Auslander–Reiten translations in monomorphism categories
  10. An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module
  11. Unitals over composition algebras
  12. Separation of bi-harmonic differential operators on Riemannian manifolds
https://doi.org/10.1515/forum-2013-0127
Schlagwörter für diesen Artikel
Separation; bi-harmonic differential operator; Riemannian manifolds

Artikel in diesem Heft

  1. Frontmatter
  2. Smooth global solutions for the two-dimensional Euler Poisson system
  3. Primitive ideals in quantum Schubert cells: Dimension of the strata
  4. Group valued null sequences and metrizable non-Mackey groups
  5. The splitting relation for Fréchet spaces over non-archimedean fields
  6. Bloch–Kato pro-p groups and locally powerful groups
  7. On Lp resolvent estimates for Laplace–Beltrami operators on compact manifolds
  8. The Ext functor and self-sums
  9. Auslander–Reiten translations in monomorphism categories
  10. An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module
  11. Unitals over composition algebras
  12. Separation of bi-harmonic differential operators on Riemannian manifolds
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