Towards a reversed Faber–Krahn inequality for the truncated Laplacian
Isabeau BirindelliUniversità di Roma La Sapienza, Italy
Giulio GaliseUniversità di Roma La Sapienza, Italy
Hitoshi IshiiTsuda University, Tokyo, Japan
We consider the nonlinear eigenvalue problem, with Dirichlet boundary condition, for the very degenerate elliptic operator mapping a function 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.
Cite this article
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii, Towards a reversed Faber–Krahn inequality for the truncated Laplacian. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 723–740DOI 10.4171/RMI/1146