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<p>We investigate eigenvalues of a class of elliptic differential operators in divergence form on compact Riemannian manifolds with boundary (possibly empty) and using Yang’s method, we prove a general inequality for these eigenvalues. By applying this inequality, we investigate universal estimates for them on compact domains of complete submanifolds in a Euclidean space, and we find inequalities for eigenvalues of special cases of these operators on compact domain of complete manifolds admitting special functions. We find universal bounds on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((k+1)\)</EquationSource> </InlineEquation>th eigenvalue according to the first <i>k</i> eigenvalues independent of the domains.</p>

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Universal Inequality for Eigenvalues of a Class of Elliptic Operators in Divergence Form

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Shahroud Azami,
  • Ghodratallah Fasihi-Ramandi,
  • Vahid Pirhadi

摘要

We investigate eigenvalues of a class of elliptic differential operators in divergence form on compact Riemannian manifolds with boundary (possibly empty) and using Yang’s method, we prove a general inequality for these eigenvalues. By applying this inequality, we investigate universal estimates for them on compact domains of complete submanifolds in a Euclidean space, and we find inequalities for eigenvalues of special cases of these operators on compact domain of complete manifolds admitting special functions. We find universal bounds on the \((k+1)\) th eigenvalue according to the first k eigenvalues independent of the domains.