4 papers
Bifurcations in Isoperimetric Problems with Nonlocal Interactions
Fabio De Regibus, Massimo Grossi, Monica Musso
We study isoperimetric problems modeled on the liquid drop model, with nonlocal interactions under a volume constraint. While balls are natural critical points, we show that, for a…
On the critical points of solutions of Robin boundary problems
Fabio De Regibus, Massimo Grossi
In this paper we prove the uniqueness of the critical point for stable solutions of the Robin problem \[ \begin{cases} -Δu=f(u)&\text{in }Ω\\ u>0&\text{in }Ω\\ \partial_νu+βu=0&\te…
On the shape of solutions to elliptic equations in possibly non convex planar domains
Luca Battaglia, Fabio De Regibus, Massimo Grossi
In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem - Delta u = f(x,y…
Uniqueness of the critical point for semi-stable solution in
Fabio De Regibus, Massimo Grossi, Debangana Mukherjee
In this paper we show the uniqueness of the critical point for \emph{semi-stable} solutions of the problem $$\begin{cases} -Δu=f(u)&\text{in }Ω\\ u>0&\text{in }Ω\\ u=0&\text{on } \…