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arXiv · 2603.05245

Estimates of eigenvalues of elliptical differential problems in divergence form

Marcio C. Araújo Filho·Juliana F. R. Miranda·Cristiano S. Silva
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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 Lam\'e 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.

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Marcio C. Araújo Filho, Juliana F. R. Miranda, Cristiano S. Silva. 2026-03-05. Estimates of eigenvalues of elliptical differential problems in divergence form. https://arxiv.org/abs/2603.05245

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