Estimates of eigenvalues of elliptical differential problems in divergence form

Abstract

In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lamé and the Laplacian operator. Furthermore, we also give universal estimates of eigenvalues for a class of fourth-order elliptic differential problems in divergence form, which encloses the well-known bi-Laplacian operator. In both cases, as applications, we obtain the gap between consecutive eigenvalues as well as an upper bound for each eigenvalue.

Theorems & Definitions (8)

• proof
• proof : Proof of Theorem \ref{['theorem1.1']}
• proof : Proof of Theorem \ref{['theorem1.2']}
• proof : Proof of Corollary \ref{['Cor_1']}
• proof
• proof : Proof of Theorem\ref{['theorem1.3']}
• proof : Proof of Corollary \ref{['cor_1.3']}
• proof : Proof of Corollary \ref{['cor_1.4']}