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：

Araujo Filho, Marcio C. ^{[1
]}

Gomes, Jose N. V. ^{[2
]}

机构：

[1] Univ Fed Rondonia, Dept Matemat, Campus Ji Parana R Rio Amazonas 351, BR-76900726 Ji Parana, RO, Brazil

[2] Univ Fed Sao Carlos, Dept Matemat, Rod Washington Luiz,Km 235, BR-13565905 Sao Carlos, SP, Brazil

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2023年 / 74卷 / 04期

关键词：

Eigenvalue estimates; Elliptic operator; Riemannian Manifold; Gaussian soliton; TRACE IDENTITIES; INEQUALITIES; LAPLACIAN; HYPERSURFACES; BOUNDS;

D O I：

10.1007/s00033-023-02054-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 Polya.

引用

页数：16

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