WG4 Research Seminar - Talk by Lorenzo Brasco

On February 23rd, 2022, Prof. Dr. Lorenzo Brasco (University Ferrara) will give a talk at 2:30 pm CET about

"Principal frequencies and inradius".

The talk will be held online in Zoom as part of the research seminar Analysis of the FernUniversität in Hagen. The zoom URL will be sent to all members of the WG4 and to all further colleagues who send a mail to Delio Mugnolo.

Abstract

We consider the first eigenvalue of the Dirichlet-Laplacian in an open set, possibly unbounded. We focus on obtaining geometric estimates for this object, in terms of the inradius (i.e. the radius of a largest ball contained in the set). We review some classical results and discuss some open problems. We then present the natural counterparts of these results for the case of the fractional Dirichlet-Laplacian.

Some of the results presented are contained in a paper written in collaboration with Francesca Bianchi (Parma).