Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds

被引：28

作者：

do Carmo, Manfredo P. ^{[2
]}

Wang, Qiaoling ^{[1
]}

Xia, Changyu ^{[1
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Inst Matematica Pura & Aplicada, BR-2246032 Rio De Janeiro, Brazil

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2010年 / 189卷 / 04期

关键词：

Universal bounds; Eigenvalues; Elliptic operator; Payne-Polya-Weinberger-Yang type inequalities; Submanifolds; Hypersurfaces in space forms; Warped manifolds; MEAN-CURVATURE; 1ST EIGENVALUE; UPPER-BOUNDS; LAPLACIAN; HYPERSURFACES; STABILITY; SPACES; GAPS;

D O I：

10.1007/s10231-010-0129-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study eigenvalues of elliptic operators in divergence form on compact Riemannian manifolds with boundary (possibly empty) and obtain a general inequality for them. By using this inequality, we prove universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds in a Euclidean space, and of complete manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to a sphere.

引用

页码：643 / 660

页数：18

共 50 条

[1] Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
Manfredo P. do Carmo
Qiaoling Wang
Changyu Xia
[J]. Annali di Matematica Pura ed Applicata, 2010, 189 : 643 - 660
[2] Inequalities for eigenvalues of fourth order elliptic operators in divergence form on Riemannian manifolds
Azami, Shahroud
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 481 (02)
[3] Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds
Araujo Filho, Marcio C.
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (02):
[4] Inequalities for lower order eigenvalues of second order elliptic operators in divergence form on Riemannian manifolds
Sun, He-Jun
Chen, Da-Guang
[J]. ARCHIV DER MATHEMATIK, 2013, 101 (04) : 381 - 393
[5] Inequalities for eigenvalues of fourth-order elliptic operators in divergence form on complete Riemannian manifolds
Marcio C. Araújo Filho
[J]. Zeitschrift für angewandte Mathematik und Physik, 2022, 73
[6] Inequalities for lower order eigenvalues of second order elliptic operators in divergence form on Riemannian manifolds
He-Jun Sun
Da-Guang Chen
[J]. Archiv der Mathematik, 2013, 101 : 381 - 393
[7] Inequalities for eigenvalues of operators in divergence form on Riemannian manifolds isometrically immersed in Euclidean space
Silva, Cristiano S.
Miranda, Juliana F. R.
Filho, Marcio C. Araujo
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 531 (01)
[8] Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds
Tan, Shenyang
Huang, Tiren
Zhang, Wenbin
[J]. ADVANCES IN MATHEMATICAL PHYSICS, 2015, 2015
[9] On Variational Inequalities Driven by Elliptic Operators Not in Divergence Form
Matzeu, Michele
Servadei, Raffaella
[J]. ADVANCED NONLINEAR STUDIES, 2012, 12 (03) : 597 - 619
[10] 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):

← 1 2 3 4 5 →