Oberseminar Analysis Winter 2026/27

We present a variational definition of the essential spectrum suitable for nonlinear operators such as the Dirichlet p-Laplacian. We then provide a geometric characterisation of the bottom of the essential spectrum by extending Persson's theorem to this framework. Finally, we show that the Ljusternik-Schnirelmann minmax levels of the constrained p-Dirichlet integral are attained whenever one of these levels is below Persson's threshold. This is based on joint work with Lorenzo Brasco, Giovanni Franzina, and Francesca Prinari.