Camilla Chiara Polvara

activity

20242026

collaborators

5 papers

math.AP2026

Regularity results for elliptic equations on cones

Carlo Alberto Antonini, Filomena Pacella, Camilla Chiara Polvara +1

We study global regularity of solutions to Dirichlet or Neumann elliptic problems in spherical sectors $S_{D, R}$ of radius $R > 0$ in $R^{N}, N \geq 2$ , where $D$ is the bounded…

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

Stability for the Sobolev inequality in cones

Filomena Pacella, Giulio Ciraolo, Camilla Chiara Polvara

We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobol…

math.AP2024

On the classification of extremals of Caffarelli-Kohn-Nirenberg inequalities

Giulio Ciraolo, Camilla Chiara Polvara

We consider a family of critical elliptic equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities, possibly in convex cones in $R^{d}$ …

math.AP2024

Classification results, rigidity theorems and semilinear PDEs on Riemannian manifolds: a P-function approach

Giulio Ciraolo, Alberto Farina, Camilla Chiara Polvara

We consider solutions to some semilinear elliptic equations on complete noncompact Riemannian manifolds and study their classification as well as the effect of their presence on th…