ON THE STRICT MONOTONICITY OF THE FIRST EIGENVALUE OF THE p-LAPLACIAN ON ANNULI

被引：15

作者：

Anoop, T., V ^{[1
]}

Bobkov, Vladimir ^{[2
,3
]}

Sasi, Sarath ^{[4
,5
]}

机构：

[1] Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India

[2] Univ West Bohemia, Fac Appl Sci, Dept Math, Univ 8, Plzen 30614, Czech Republic

[3] Univ West Bohemia, Fac Appl Sci, NTIS, Univ 8, Plzen 30614, Czech Republic

[4] HBNI, Natl Inst Sci Educ & Res Bhubaneswar, Sch Math Sci, Jatni 752050, India

[5] Indian Inst Technol Palakkad, Ahalia Integrated Campus, Palakkad 678557, Kerala, India

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 10期

关键词：

p-Laplacian; symmetries; shape derivative; Fucik spectrum; eigenvalue; eigenfunction; nonradiality; NODAL SOLUTIONS; INEQUALITIES; DOMAINS;

D O I：

10.1090/tran/7241

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B-1 be a ball in R-N centred at the origin and let B-0 be a smaller ball compactly contained in B-1. For p is an element of (1, infinity), using the shape derivative method, we show that the first eigenvalue of the p-Laplacian in annulus B-1 \ (B-0) over bar strictly decreases as the inner ball moves towards the boundary of the outer ball. The analogous results for the limit cases as p -> 1 and p -> infinity are also discussed. Using our main result, further we prove the nonradiality of the eigenfunctions associated with the points on the first nontrivial curve of the Fu. cik spectrum of the p-Laplacian on bounded radial domains.

引用

页码：7181 / 7199

页数：19

共 25 条

[1] ON THE STRUCTURE OF THE SECOND EIGENFUNCTIONS OF THE p-LAPLACIAN ON A BALL [J].

Anoop, T. V. ;

Drabek, P. ;

Sasi, Sarath .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (06) :2503-2512

[2]

Ashbaugh MS, 2007, P SYMP PURE MATH, V76, P105

[3]

Barles G., 1988, Annales de la Facult des sciences de Toulouse, V9, P65

[4] Partial symmetry of least energy nodal solutions to some variational problems [J].

Bartsch, T ;

Weth, T ;

Willew, M .

JOURNAL D ANALYSE MATHEMATIQUE, 2005, 96 (1) :1-18

[5]

Bartsch T, 2006, REND LINCEI-MAT APPL, V17, P69

[6] The first nontrivial curve in the fuA0k spectrum of the dirichlet laplacian on the ball consists of nonradial eigenvalues [J].

Benedikt, Jirl ;

Drabek, Pavel ;

Girg, Petr .

BOUNDARY VALUE PROBLEMS, 2011, :1-9

[7] On the p-torsion functions of an annulus [J].

Bueno, H. ;

Ercole, G. .

ASYMPTOTIC ANALYSIS, 2015, 92 (3-4) :235-247

[8] An eigenvalue optimization problem for the p-Laplacian [J].

Chorwadwala, Anisa M. H. ;

Mahadevan, Rajesh .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (06) :1145-1151

[9] ON THE FABER-KRAHN INEQUALITY FOR THE DIRICHLET p-LAPLACIAN [J].

Chorwadwala, Anisa M. H. ;

Mahadevan, Rajesh ;

Toledo, Francisco .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2015, 21 (01) :60-72

[10] The beginning of the Fucik spectrum for the p-Laplacian [J].

Cuesta, M ;

de Figueiredo, D ;

Gossez, JP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 159 (01) :212-238

← 1 2 3 →