# Seminario: “The Biharmonic operator with tension: eigenvalues' behavior and asymptotics”

## Mercoledì 21 Febbraio 2018, ore 09:15 - Aula 2BC30 - Davide Buoso

ARGOMENTI: Seminari

Mercoledì 21 Febbraio 2018 alle ore 09:15 in Aula 2BC30, Davide Buoso (Universidade de Lisboa) terrà un seminario dal titolo “The Biharmonic operator with tension: eigenvalues' behavior and asymptotics”.

Abstract
The eigenvalues of the Biharmonic operator $\Delta^2$ have been extensively studied in the literature, and still today there are a number of open problems regarding e.g., shape optimization or positivity properties of the first eigenfunctions. In this talk we consider the Biharmonic operator with a tension term $\Delta^2+\alpha\Delta$, which recently gained interest in the mathematical community. After recalling the known results for this problem, we discuss the dependence of the eigenvalues upon the parameter \alpha as well as the asymptotic expansions. If time permits, we will also discuss other properties that depend on the parameter $\alpha$.
Joint works with P. Antunes and P. Freitas.?