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Principal eigenvalues for k-Hessian operators by maximum principle methods

Banff International Research Station for Mathematical Innovation and Discovery

For fully nonlinear k-Hessian operators on bounded strictly (k-1)-convex domains of Euclidian space, a characterization of the principal eigenvalue associated to a k-convex and negative principal eigenfunction will be given as the supremum over values of a spectral parameter for which admissible viscosity supersolutions obey a minimum principle. The admissibility condition is phrased in terms of elliptic branches in the sense of Krylov [TAMS’95] that correspond to selecting k-convex functions. Moreover, the associated principal eigenfunction is constructed by an iterative viscosity solution technique, which exploits a compactness property coming from the establishment of a global Hölder continuity property for the approximating equations. This is joint work with Isabeau Birindelli.

Mathematics; Partial differential equations; Integral equations

video/mp4

Author affiliation: Università degli Studi di Milano

2017-10-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63198

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/