Seminario di Analisi Matematica

Mercoledì 3 giugno alle ore 14:30, Camilla Polvara (Sapienza Università di Roma) terrà un Seminario di Analisi Matematica dal titolo "Critical Neumann problem in cones: bifurcation, stability, and regularity".

Abstract:
We consider the critical Neumann problem in cones. We prove that the standard bubbles, which are the only radial solutions, become unstable for a class of nonconvex cones, which is defined through the first Neumann eigenvalue of the Laplace Beltrami operator on the domain D on the unit sphere, which spans the cone. This immediately implies a symmetry breaking result for the minimizers of the Sobolev inequality. Actually, a bifurcation result from the standard bubbles can be proved. We also present a quantitative Sobolev inequality of Bianchi-Egnell type, which holds in any cone, even if the minimizers are not the standard bubbles. Finally, we study the regularity of solutions to semilinear critical equations on cones.
These results are contained in joint works with C.A. Antonini, G. Ciraolo, F. Pacella, and L. Provenzano.

Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Largo S. Leonardo Murialdo 1, aula C308.