OPTIMIZATION OF THE PRINCIPAL EIGENVALUE UNDER MIXED BOUNDARY CONDITIONS

被引：0

作者：

Cadeddu, Lucio ^{[1
]}

Farina, Maria Antonietta ^{[1
]}

Porru, Giovanni ^{[1
]}

机构：

[1] Univ Cagliari, Dipartimento Matemat & Informat, I-09124 Cagliari, Italy

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2014年

关键词：

Principal eigenvalue; rearrangements; minimization; maximization; symmetry breaking; population dynamics; COMPOSITE MEMBRANES; INDEFINITE WEIGHTS; ELLIPTIC-EQUATIONS; 1ST EIGENVALUE; REARRANGEMENTS; MAXIMIZATION; MINIMIZATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate minimization and maximization of the principal eigenvalue of the Laplacian under mixed boundary conditions in case the weight has indefinite sign and varies in a class of rearrangements. Biologically, these optimization problems are motivated by the question of determining the most convenient spatial arrangement of favorable and unfavorable resources for a species to survive or to decline. We prove existence and uniqueness results, and present some features of the optimizers. In special cases, we prove results of symmetry and results of symmetry breaking for the minimizer.

引用

页数：17

共 50 条

[1] MINIMIZATION OF THE PRINCIPAL EIGENVALUE UNDER NEUMANN BOUNDARY CONDITIONS
Jha, Kanhaiya
Porru, Giovanni
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2011, 32 (11) : 1146 - 1165
[2] Principal eigenvalue of mixed problem for the fractional Laplacian: Moving the boundary conditions
Leonori, Tommaso
Medina, Maria
Peral, Ireneo
Primo, Ana
Soria, Fernando
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (02) : 593 - 619
[3] OPTIMIZATION OF THE PRINCIPAL EIGENVALUE OF THE PSEUDO p-LAPLACIAN OPERATOR WITH ROBIN BOUNDARY CONDITIONS
Emamizadeh, B.
Zivari-Rezapour, M.
[J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 2012, 23 (12)
[4] Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Lotoreichik, Vladimir
Rohleder, Jonathan
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (01) : 491 - 508
[5] Eigenvalue variation under moving mixed Dirichlet-Neumann boundary conditions and applications
Abatangelo, L.
Felli, V
Lena, C.
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2020, 26
[6] NONLINEAR EIGENVALUE PROBLEMS WITH MIXED BOUNDARY-CONDITIONS
HEATH, JM
WAKE, GC
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 48 (03) : 721 - 735
[7] On the Lowest Eigenvalue of Laplace Operators with Mixed Boundary Conditions
Kovarik, Hynek
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2014, 24 (03) : 1509 - 1525
[8] On the Lowest Eigenvalue of Laplace Operators with Mixed Boundary Conditions
Hynek Kovařík
[J]. The Journal of Geometric Analysis, 2014, 24 : 1509 - 1525
[9] AN EIGENVALUE PROBLEM WITH MIXED BOUNDARY CONDITIONS AND TRACE THEOREMS
Bandle, Catherine
[J]. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2008, 2 (02): : 68 - 75
[10] NONLINEAR EIGENVALUE PROBLEMS WITH MIXED BOUNDARY-CONDITIONS
WAKE, GC
HEATH, JM
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (01): : A150 - A150

← 1 2 3 4 5 →