Towards a reversed Faber–Krahn inequality for the truncated Laplacian

  • Isabeau Birindelli

    Università di Roma La Sapienza, Italy
  • Giulio Galise

    Università di Roma La Sapienza, Italy
  • Hitoshi Ishii

    Tsuda University, Tokyo, Japan
Towards a reversed Faber–Krahn inequality for the truncated Laplacian cover

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Abstract

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. 723–740

DOI 10.4171/RMI/1146