Some inequalities for eigenvalues of an elliptic differential operator

Azami, Shahroud; Zohrehvand, Mosayeb; Fasihi-Ramandi, Ghodratallah

doi:10.22103/jmmr.2024.22939.1582

Some inequalities for eigenvalues of an elliptic differential operator

Document Type : Research Paper

Authors

Shahroud Azami ¹

Mosayeb Zohrehvand ²

Ghodratallah Fasihi-Ramandi ¹

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

² Department of mathematics, Malayer University, Malayer, Iran

10.22103/jmmr.2024.22939.1582

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.

Keywords

Universal bound‎

‎Elliptic operator‎

‎Eigenvalue‎

‎submanifold

Subjects

Geometry and Topology

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