A PRIORI ESTIMATE FOR THE FIRST EIGENVALUE OF THE p-LAPLACIAN

被引：0

作者：

Kajikiya, Ryuji ^{[1
]}

机构：

[1] Saga Univ, Fac Sci & Engn, Dept Math, Saga 8408502, Japan

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2015年 / 28卷 / 9-10期

关键词：

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the first eigenvalue of the p-Laplacian under the Dirichlet boundary condition. For a convex domain, we give an a priori estimate for the first eigenvalue in terms of the radius d of the maximum ball contained in the domain. As a consequence, we prove that the first eigenvalue diverges to infinity as p -> infinity if the domain is convex and d <= 1. Moreover, we show that in the annulus domain a < vertical bar x vertical bar < b, the first eigenvalue diverges to infinity if b - a <= 2 and converges to zero if b - a > 2.

引用

页码：1011 / 1028

页数：18

共 50 条

[1] Sharp estimate on the first eigenvalue of the p-Laplacian
Valtorta, Daniele
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (13) : 4974 - 4994
[2] Eigenvalue estimate for the weighted p-Laplacian
Lin Feng Wang
[J]. Annali di Matematica Pura ed Applicata, 2012, 191 : 539 - 550
[3] Eigenvalue estimate for the weighted p-Laplacian
Wang, Lin Feng
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2012, 191 (03) : 539 - 550
[4] LOWER ESTIMATE OF THE FIRST EIGENVALUE OF p-LAPLACIAN VIA HARDY INEQUALITY
Kutev, Nikolai
Rangelov, Tsviatko
[J]. COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2019, 72 (09): : 1167 - 1176
[5] LOWER ESTIMATE OF THE FIRST EIGENVALUE OF p-LAPLACIAN VIA HARDY INEQUALITY
Fabricant, Alexander
Kutev, Nikolai
Rangelov, Tsviatko
[J]. COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2015, 68 (05): : 561 - 568
[6] Boundedness of the first eigenvalue of the p-Laplacian
Matei, AM
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (07) : 2183 - 2192
[7] The first eigenvalue of Finsler p-Laplacian
Yin, Song-Ting
He, Qun
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2014, 35 : 30 - 49
[8] ON THE FIRST EIGENVALUE OF THE NORMALIZED p-LAPLACIAN
Crasta, Graziano
Fragala, Ilaria
Kawohl, Bernd
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (02) : 577 - 590
[9] On the first eigenvalue of the p-Laplacian on Riemannian manifolds
Seto, Shoo
[J]. DIFFERENTIAL GEOMETRY AND GLOBAL ANALYSIS: IN HONOR OF TADASHI NAGANO, 2022, 777 : 199 - 209
[10] FIRST EIGENVALUE OF THE p-LAPLACIAN ON KAHLER MANIFOLDS
Blacker, Casey
Seto, Shoo
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 147 (05) : 2197 - 2206

← 1 2 3 4 5 →