Revista Matemática Iberoamericana


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Published online first: 2019-09-27
DOI: 10.4171/rmi/1146

Towards a reversed Faber–Krahn inequality for the truncated Laplacian

Isabeau Birindelli[1], Giulio Galise[2] and Hitoshi Ishii[3]

(1) Università di Roma La Sapienza, Italy
(2) Università di Roma La Sapienza, Italy
(3) Tsuda University, Tokyo, Japan

We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for the very degenerate elliptic operator $\mathcal{P}^+_{1}$ 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.

Keywords: Degenerate elliptic operators, Dirichlet problems, principal eigenvalue, qualitative properties

Birindelli Isabeau, Galise Giulio, Ishii Hitoshi: Towards a reversed Faber–Krahn inequality for the truncated Laplacian. Rev. Mat. Iberoam. Electronically published on September 27, 2019. doi: 10.4171/rmi/1146 (to appear in print)