7 citations · 10 across the 19 of their papers we have counts for
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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…
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…
On various Carleson-type geometric lemmas and uniform rectifiability in metric spaces: Part 2
Katrin Fässler, Ivan Yuri Violo
We characterize uniform -rectifiability in Euclidean spaces in terms of a Carleson-type geometric lemma for a new notion of flatness coefficients, which we call -numbers. The…
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 an…