Principal eigenvalues for <i>k</i>-Hessian operators by maximum principle methods

For fully nonlinear $k$-Hessian operators on bounded strictly $(k-1)$-convex domains $\Omega$ of $\mathbb{R}^N$, a characterization the principal eigenvalue associated to $k$-convex and negative eigenfunction will be given as supremum over values spectral parameter for which admissible viscosity supersolutions obey minimum principle. The admissibility condition is phrased in terms natural closed convex cone $\Sigma_k \subset {\cal S}(N)$ an elliptic set sense Krylov [23] corresponds using functions constraints formulation subsolutions supersolutions. Moreover, constructed by iterative solution technique, exploits compactness property results from establishment global Hölder estimate unique solutions approximating equations.