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

被引：0
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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;
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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.
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