A spectral characterization and an approximation scheme for the Hessian eigenvalue
Nam Q. Le
Indiana University, Bloomington, USA
![A spectral characterization and an approximation scheme for the Hessian eigenvalue cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-38-issue-5.png&w=3840&q=90)
Abstract
We revisit the -Hessian eigenvalue problem on a smooth and bounded -convex domain in . First, we obtain a spectral characterization of the -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 -Hessian operator. We show that the scheme converges, with a rate, to the -Hessian eigenvalue for all . When , we also prove a local convergence of the Hessian of solutions of the scheme. Hyperbolic polynomials play an important role in our analysis.
Cite this article
Nam Q. Le, A spectral characterization and an approximation scheme for the Hessian eigenvalue. Rev. Mat. Iberoam. 38 (2022), no. 5, pp. 1473–1500
DOI 10.4171/RMI/1306