44 citations · 128 across the 34 of their papers we have counts for
37 papers · 1 filter
Qualitative properties of eigenfunctions in domains with small holes
Laura Abatangelo, Massimo Grossi, Ying Li
In this paper we study qualitative properties of the eigenvalues and eigenfunctions of with Dirichlet boundary condition in a smooth bounded domain with a small circular h…
On the critical points of solutions of PDE in a non-convex settings: the case of concentrating solutions
Francesca Gladiali, Massimo Grossi
In this paper we are concerned with the number of critical points of solutions of nonlinear elliptic equations. We will deal with the case of non-convex, contractile and non-contra…
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…
Qualitative analysis on the critical points of the Robin function
Francesca Gladiali, Massimo Grossi, Peng Luo +1
Let be a smooth bounded domain with and where is the ball centered at and radius . In this paper, we est…
On the number of critical points of the second eigenfunction of the Laplacian in convex planar domains
Fabio De Regibus, Massimo Grossi
In this paper we consider the second eigenfunction of the Laplacian with Dirichlet boundary conditions in convex domains. If the domain has \emph{large eccentricity} then the eigen…
Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two
Massimo Grossi, Isabella Ianni, Peng Luo +1
We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -Δu=u^{p} &{\text{in}~Ω},\\[0.5mm] u>0 &{\text{in}~Ω},\\[0.5mm] u=0 &{\text{on}~\partial Ω}, \end{cases…