THE PRINCIPAL EIGENVALUE OF THE ∞-LAPLACIAN WITH THE NEUMANN BOUNDARY CONDITION

被引：6

作者：

Patrizi, Stefania ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2011年 / 17卷 / 02期

关键词：

infinity-Laplacian; Neumann boundary condition; principal eigenvalue; viscosity solutions; VISCOSITY SOLUTIONS; MAXIMUM PRINCIPLE; BIFURCATION; OPERATORS;

D O I：

10.1051/cocv/2010019

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We prove the existence of a principal eigenvalue associated to the infinity-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.

引用

页码：575 / 601

页数：27

共 50 条

[1] On domain monotonicity for the principal eigenvalue of the Laplacian with a mixed Dirichlet-Neumann boundary condition
Pinsky, RG
[J]. Geometry, Spectral Theory, Groups, and Dynamics, 2005, 387 : 245 - 252
[2] On the lowest eigenvalue of the Laplacian with Neumann boundary condition at a small obstacle
Hempel, R
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 194 (01) : 54 - 74
[3] ON THE EIGENVALUE SET OF THE (p, q)-LAPLACIAN WITH A NEUMANN-STEKLOV BOUNDARY CONDITION
Barbu, Luminita
Morosanu, Gheorghe
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2023, 36 (5-6) : 437 - 452
[4] THE ANISOTROPIC ∞-LAPLACIAN EIGENVALUE PROBLEM WITH NEUMANN BOUNDARY CONDITIONS
Piscitelli, Gianpaolo
[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS, 2019, 32 (11-12) : 705 - 734
[5] On Laplacian eigenvalue equation with constant Neumann boundary data
Huang, Yong
Li, Qinfeng
Li, Qiuqi
Yao, Ruofei
[J]. MATHEMATISCHE ANNALEN, 2024,
[6] ON THE FIRST NONTRIVIAL EIGENVALUE OF THE ∞LAPLACIAN WITH NEUMANN BOUNDARY CONDITIONS
Rossi, J. D.
Saintier, N.
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2016, 42 (02): : 613 - 635
[7] MINIMIZATION OF THE PRINCIPAL EIGENVALUE UNDER NEUMANN BOUNDARY CONDITIONS
Jha, Kanhaiya
Porru, Giovanni
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2011, 32 (11) : 1146 - 1165
[8] The Neumann eigenvalue problem for the ∞-Laplacian
Esposito, L.
Kawohl, B.
Nitsch, C.
Trombetti, C.
[J]. RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2015, 26 (02) : 119 - 134
[9] ON EIGENVALUE PROBLEMS OF THE P-LAPLACIAN WITH NEUMANN BOUNDARY-CONDITIONS
HUANG, YX
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 109 (01) : 177 - 184
[10] Eigenvalue problem in two dimensions for an irregular boundary: Neumann condition
S. Panda
S. Chakraborty
S. P. Khastgir
[J]. The European Physical Journal Plus, 126

← 1 2 3 4 5 →