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.
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页码：723 / 740
页数：18
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