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
- DOI: 10.4171/RMI/1306
- Enlaces
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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
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