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Quantitative stability in distribution for the Sobolev inequality under curvature dimension condition
Max Fathi, Ivan Yuri Violo
The goal of this note is to investigate quantitative stability properties of the critical Sobolev inequality in metric measure spaces. Assuming that the optimal c…
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…
Regularity for quasilinear elliptic equations in metric measure spaces
Simon Schulz, Ivan Yuri Violo
In the present article we prove second-order and Lipschitz regularity for quasilinear elliptic equations in metric spaces endowed with a lower bound on the Ricci curvature. The est…
Fine Pólya-SzegŠrearrangement inequalities in metric spaces and applications
Francesco Nobili, Ivan Yuri Violo
We study fine Pólya-SzegÅ rearrangement inequalities into weighted intervals for Sobolev functions and functions of bounded variation defined on metric measure spaces supporting…
An overview of regularity results for the Laplacian and -Laplacian in metric spaces
Ivan Yuri Violo
We review some regularity results for the Laplacian and -Laplacian in metric measure spaces. The focus is mainly on interior Hölder, Lipschitz and second-regularity estimates a…