3 papers
math.AP2025
Bifurcation from bubbles in nonconvex cones
Filomena Pacella, Camilla Chiara Polvara, Luigi Provenzano
We investigate the Neumann problem for the critical semilinear elliptic equation in cones. The standard bubble provides a family of radial solutions, which are known to be the only…
math.AP2025
The role of the curvature of a surface in the shape of the solutions to elliptic equations
Francesca Gladiali, Massimo Grossi, Luigi Provenzano
We prove uniqueness and non-degeneracy of the critical point of positive, semi-stable solutions of with Dirichlet boundary conditions for a class of star-shaped domains…
math.AP2025
A note on the first Steklov eigenvalue on planar domains
Azahara DelaTorre, Gabriele Mancini, Angela Pistoia +1
We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second…