Lower Bounds for Eigenvalues of Elliptic Operators by Overlapping Domain Decomposition

Lower Bounds for Eigenvalues of Elliptic Operators: By Nonconforming Finite Element Methods

The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation properties of nonconforming finite element spaces Vh are better than global continuity properties of Vh, corresponding methods will produce lower bounds for eigenvalu...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Estimates for the First Nonzero Eigenvalue of Elliptic Operators in Divergence Form

We consider elliptic operators in divergence form L = div (Φ · grad ) either on a closed Riemannian manifold or in a domain with compact closure and piecewise smooth boundary M where Φ : M → End(TM) is a positive definite symmetric smooth section of the bundle of all endomorphisms of TM . We show that the first nonzero L-eigenvalues in the closed or Dirichlet eigenvalue problems can be bounded ...

Fundamental tone estimates for elliptic operators in divergence form and geometric applications.

We establish a method for giving lower bounds for the fundamental tone of elliptic operators in divergence form in terms of the divergence of vector fields. We then apply this method to the Lr operator associated to immersed hypersurfaces with locally bounded (r + 1)-th mean curvature Hr + 1 of the space forms Nn+ 1(c) of constant sectional curvature c. As a corollary we give lower bounds for t...