Noah Piemontese-Fischer University Bonn
A degenerate incompatible two-well problem related to quadrature domains and Hele-Shaw flows
In this talk, we study an incompatible two-well problem that exhibits some surprising flexibility properties. We consider two variants of the problem: one without gauge invariance and one with SO(2) invariance. Upon taking a glimpse at the relaxations of the energies, we discuss a connection between these variational problems and the theory of quadrature domains. This link allows us to construct minimizers with finite surface energy via tools from potential theory and free-boundary problems, including partial balayage, mother bodies and a squeezing-type Hele-Shaw flow. The talk is based on ongoing joint work with Lennart Machill and Angkana Rüland.
Thursday, November 12, at 14:15 in Lipschitz-Saal
Dr. Luca Briani (TUM)
Spectrum of the p−Laplacian on general open sets
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.
