Eigenvalue estimates for a class of elliptic differential operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space

被引：0

作者：

Marcio C. Araújo Filho

José N. V. Gomes

机构：

[1] Universidade Federal de Rondônia,Departamento de Matemática

[2] Universidade Federal de São Carlos,Departamento de Matemática

来源：

Zeitschrift für angewandte Mathematik und Physik | 2023年 / 74卷

关键词：

Eigenvalue estimates; Elliptic operator; Riemannian Manifold; Gaussian soliton; Primary 47A75; Secondary 47F05; 35P15; 53C25;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We obtain eigenvalue estimates for a larger class of elliptic differential operators in divergence form on a bounded domain in a complete Riemannian manifold isometrically immersed in Euclidean space. As an application, we give eigenvalue estimates in the Gaussian shrinking soliton, and we find a domain that makes the behavior of these estimates similar to the estimates for the case of the Laplacian. Moreover, we also give an answer to the generalized conjecture of Pólya.

引用

共 50 条

[1] Eigenvalue estimates for a class of elliptic differential operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space
Araujo Filho, Marcio C.
Gomes, Jose N. V.
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2023, 74 (04):
[2] Inequalities for eigenvalues of operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space
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Miranda, Juliana F. R.
Filho, Marcio C. Araujo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 531 (01)
[3] Eigenvalue estimates for a class of elliptic differential operators in divergence form
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