Stability in Gagliardo-Nirenberg inequalities

The fast diffusion equation determines the family of inequalities, which in- cludes Sobolev’s inequality as an endpoint, and dictates the functional setting and the strategy,

There is a also notion of gradient flow for a well-chosen notion of distance (which is not, in general, Wasserstein’s distance), that is studied in Section 6.2 and for which

Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation (supplementary material).

B Stability in a weaker norm but with explicit constants B From duality to improved estimates based on Yamabe’s flow.. Dolbeault Stability in

We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, as well as a sharp weighted trace Sobolev inequality on epigraphs of convex functions... With

One is to establish an abstract convex Sobolev type inequality using mass transport, and the other one is to establish a new functional Brunn-Minkowski type inequality on R n + ,

N = 1, Ω = R.. The proof consists of a tedious analysis of all possibilities. Apply Corollary 3.1. Here we use again reiteration. There is nothing to prove! Case 9.. This follows

[2] for equiva- lent statements on heat kernel functional inequalities; see also [8,3,7] for a parabolic Harnack inequality using the dimension–curvature condition by shifting