The principal eigenvalue and the maximum principle for degenerate elliptic operators

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 15:00

Relatore:

• Italo Capuzzo Dolcetta (Università di Roma)

Abstract:

I will report on research in collaboration with Berestycki, Porretta and Rossi [1] and with Birindelli and Camilli [2]. An extended notion of principal eigenvalue is introduced in [1] in the general framework of fully nonlinear degenerate elliptic operators; the positivity of this number is shown to be equivalent to the validity of the maximum principle (or sign propagation property). Under stronger ellipticity conditions we proposed in [2] some finite differences schemes to compute this number by means of Collatz-Wielandt type formula. It is worth to point out that numerical approaches to the computation of eigenvalues are usually based on finite elements approximations of the classical Rayleigh-Ritz formula, therefore requiring divergence structure of the operator which is not assumed in our approach.
[1] H. Berestycki, A. Porretta, L. Rossi, ICD, Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators, JMPA 2014
[2] I. Birindelli, F. Camilli, ICD, On the approximation of the principal eigenvalue for a class of nonlinear elliptic operators, submitted

Referente: Luciano Tubaro