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.
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页数：16
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