Inequalities for eigenvalues of fourth order elliptic operators in\n divergence form on Riemannian manifolds

2019/01/30 by Shahroud Azami, Azami, Shahroud
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1901.11018

Abstract

In this paper, we study eigenvalue of linear fourth order elliptic operators\nin divergence form with Dirichlet boundary condition on a bounded domain in a\ncompact Riemannian manifolds with boundary (possibly empty) and find a general\ninequality for them. As an application, by using this inequality, we study\neigenvalues of this operator on compact domains of complete submanifolds in a\nEuclidean space.\n

Related

• Inequalities for eigenvalues of operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space
• Estimates of the gaps between consecutive eigenvalues for a class of elliptic differential operators in divergence form on Riemannian manifolds
• Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains
• The Levine--Weinberger and Friedlander--Filonov inequalities for some classes of elliptic operators
• Estimates for eigenvalues of the operator L_r