10 papers · 1 filter
Nontrivial solutions to the relative overdetermined torsion problem in a cylinder
Filomena Pacella, David Ruiz, Pieralberto Sicbaldi
Given a bounded regular domain and the half-cylinder , we consider the relative overdetermined torsion problem in , i.e. \[\l…
Optimal quantitative stability for a Serrin-type problem in convex cones
Filomena Pacella, Giorgio Poggesi, Alberto Roncoroni
We consider a Serrin-type problem in convex cones in the Euclidean space and motivated by recent rigidity results we study the quantitative stability issue for this problem. In par…
Energy stability for a class of semilinear elliptic problems
Danilo Gregorin Afonso, Alessandro Iacopetti, Filomena Pacella
In this paper, we consider semilinear elliptic problems in a bounded domain contained in a given unbounded Lipschitz domain . Our aim is to stud…
Symmetry breaking and instability for semilinear elliptic equations in spherical sectors and cones
Giulio Ciraolo, Filomena Pacella, Camilla Chiara Polvara
We consider semilinear elliptic equations with mixed boundary conditions in spherical sectors inside a cone. The aim of the paper is to show that a radial symmetry result of Gidas-…
Morse Index and Symmetry for Elliptic Problems with Nonlinear Mixed Boundary Conditions
Lucio Damascelli, Filomena Pacella
Under a Morse index condition we prove symmetry results for solutions of a nonlinear mixed boundary condition elliptic problem. As an intermediate step we relate the Morse index of…
Existence results for fully nonlinear equations in radial domains
Giulio Galise, Fabiana Leoni, Filomena Pacella
We consider the fully nonlinear problem \begin{equation*} \begin{cases} -F(x,D^2u)=|u|^{p-1}u & \text{in }\\ u=0 & \text{on } \end{cases} \end{equation*} where is…