BOUNDS FOR EIGENFUNCTIONS OF THE LAPLACIAN ON NONCOMPACT RIEMANNIAN MANIFOLDS

被引：9

作者：

Cianchi, Andrea ^{[1
]}

Maz'ya, Vladimir G. ^{[2
,3
]}

机构：

[1] Univ Florence, Dipartimento Matemat & Informat Ulisse Dini, I-50122 Florence, Italy

[2] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England

[3] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2013年 / 135卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

ISOPERIMETRIC-INEQUALITIES; SOBOLEV INEQUALITIES; EIGENVALUE; THEOREMS; SPECTRUM; CONSTANTS; SURFACES;

D O I：

10.1353/ajm.2013.0028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds M of finite volume. Sharp conditions ensuring L-q(M) and L-infinity(M) bounds for eigenfunctions are exhibited in terms of either the isoperimetric function or the isocapacitary function of M.

引用

页码：579 / 635

页数：57

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