5 papers · 1 filter
Divergence-free concentrations come from vanishing sequences
Adolfo Arroyo-Rabasa, Francesco Nobili, Ivan Yuri Violo
A vanishing sequence of divergence-free matrix fields is one that is bounded in and is carried by open sets of vanishing volume. Recently established, Bouchitté's…
Generalized existence of extremizers for the sharp -Sobolev inequality on Riemannian manifolds with nonnegative curvature
Francesco Nobili, Ivan Yuri Violo
We study the generalized existence of extremizers for the sharp -Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean vol…
An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds
Francesco Nobili
We review recent results regarding the problem of the stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and…
Fine Pólya-Szegő rearrangement inequalities in metric spaces and applications
Francesco Nobili, Ivan Yuri Violo
We study fine Pólya-Szegő rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting an…
Quantitative stability of Sobolev inequalities on compact Riemannian manifolds
Francesco Nobili, Davide Parise
We study quantitative stability results for different classes of Sobolev inequalities on general compact Riemannian manifolds. We prove that, up to constants depending on the manif…