Towards a reversed Faber-Krahn inequality for the truncated Laplacian

被引：9

作者：

Birindelli, Isabeau ^{[1
]}

Galise, Giulio ^{[1
]}

Ishii, Hitoshi ^{[2
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Matemat G Castelnuovo, Ple Aldo Moro 2, I-00185 Rome, Italy

[2] Tsuda Univ, Inst Math & Comp Sci, 2-1-1 Tsuda Machi, Kodaira, Tokyo 1878577, Japan

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2020年 / 36卷 / 03期

关键词：

Degenerate elliptic operators; Dirichlet problems; principal eigenvalue; qualitative properties; PRINCIPAL EIGENVALUE; VISCOSITY SOLUTIONS; MAXIMUM PRINCIPLE;

D O I：

10.4171/RMI/1146

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for the very degenerate elliptic operator P-1(+) mapping a function u to the maximum eigenvalue of its Hessian matrix. The aim is to show that, at least for square type domains having fixed volume, the symmetry of the domain maximizes the principal eigenvalue, contrary to what happens for the Laplacian.

引用

页码：723 / 740

页数：18

共 50 条

[21] The ∞-capacity and Faber-Krahn inequality on Grushin spaces
Li, Guoliang
Liu, Yu
MONATSHEFTE FUR MATHEMATIK, 2021, 196 (01): : 135 - 162
[22] Uniqueness in the Faber-Krahn inequality for Robin problems
Daners, Daniel
Kennedy, James
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2007, 39 (04) : 1191 - 1207
[23] Is the Faber-Krahn inequality true for the Stokes operator?
Henrot, Antoine
Mazari-Fouquer, Idriss
Privat, Yannick
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2024, 63 (09)
[24] Faber-Krahn type inequality for unicyclic graphs
Zhang, Guang-Jun
Zhang, Jie
Zhang, Xiao-Dong
LINEAR & MULTILINEAR ALGEBRA, 2012, 60 (11-12): : 1355 - 1364
[25] A local Faber-Krahn inequality and applications to Schrodinger equations
Lierl, Janna
Steinerberger, Stefan
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2018, 43 (01) : 66 - 81
[26] A Faber-Krahn inequality for solutions of Schrodinger's equation
De Carli, L.
Hudson, S. M.
ADVANCES IN MATHEMATICS, 2012, 230 (4-6) : 2416 - 2427
[27] A Faber-Krahn Inequality for the Cheeger Constant of N -gons
Bucur, Dorin
Fragala, Ilaria
JOURNAL OF GEOMETRIC ANALYSIS, 2016, 26 (01) : 88 - 117
[28] An alternative approach to the Faber-Krahn inequality for Robin problems
Bucur, Dorin
Daners, Daniel
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 37 (1-2) : 75 - 86
[29] A Faber-Krahn inequality for mixed local and nonlocal operators
Stefano Biagi
Serena Dipierro
Enrico Valdinoci
Eugenio Vecchi
Journal d'Analyse Mathématique, 2023, 150 : 405 - 448
[30] A quantitative stability estimate for the fractional Faber-Krahn inequality
Brasco, Lorenzo
Cinti, Eleonora
Vita, Stefano
JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 279 (03)

← 1 2 3 4 5 →