Towards a reversed Faber–Krahn inequality for the truncated Laplacian

Isabeau Birindelli ^[2] ; Giulio Galise ^[2] ; Hitoshi Ishii ^[1]
1. [1] Tsuda College
  
  Tsuda College
  
  Japón
2. [2] Università di Roma La Sapienza
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 3, 2020, págs. 723-740
Idioma: inglés
DOI: 10.4171/rmi/1146
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Resumen
- 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.