Some inequalities for eigenvalues of an elliptic differential operator

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran.

2 Department of mathematics, Malayer University, Malayer, Iran

Abstract

‎In the present paper, we investigate  the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates  for eigenvalues on compact domains of  complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on  the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of  the domains.

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References

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Journal of Mahani Mathematical Research
Volume 14, Issue 1 - Serial Number 31
January 2025
Pages 137-154

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History

  • Receive Date: 12 February 2024
  • Revise Date: 22 June 2024
  • Accept Date: 18 August 2024

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