A spectral characterization and an approximation scheme for the Hessian eigenvalue

• Autores: Nam Q. Le
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 5, 2022, págs. 1473-1500
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We revisit the kk-Hessian eigenvalue problem on a smooth and bounded {(k-1)}(k−1)-convex domain in \mathbb{R}^nRn. First, we obtain a spectral characterization of the kk-Hessian eigenvalue as the infimum of the first eigenvalues of linear second-order elliptic operators whose coefficients belong to the dual of the corresponding Gårding cone. Second, we introduce a non-degenerate inverse iterative scheme to solve the eigenvalue problem for the kk-Hessian operator. We show that the scheme converges, with a rate, to the kk-Hessian eigenvalue for all kk. When 2\leq k\leq n2≤k≤n, we also prove a local L^1L1 convergence of the Hessian of solutions of the scheme. Hyperbolic polynomials play an important role in our analysis