Séminaire d'Analyse

Valeurs propres variationnels et non-variationnels du p-Laplacien
Peter Takac
Thursday 08 March 2012 11:00 -  Tours -  Salle 2290 (Bât E2)

Résumé :
We begin this lecture with a discussion of the famous Ljusternik-Schnirelmann characterization of some eigenvalues of nonlinear elliptic problems (by a minimax formula) which has a global variational character. Then we show that for some homogeneous quasi-linear elliptic eigenvalue problems there are variational eigenvalues other than those of the Ljusternik-Schnirelmann-type. In contrast, these eigenvalues have a local variational character. Such phenomenon does not occur in typical linear elliptic eigenvalue problems, thanks to the Courant-Fischer theorem which is the linear analogue and predecessor of the Ljusternik-Schnirelmann theory. Finally, we will show some hints for proofs which combine variational and topological methods with linearization procedures. Keywords: nonlinear homogeneous eigenvalue problem, Ljusternik-Schnirelmann characterization, local variational characterization, $p$-Laplacian

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