Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation

Our main result, see Theorem 1, is that the Cauchy-Born rule applies, up to a small error that we estimate in terms of the two-body potential of interaction.. From a mathematical

Sobolev spaces; Hardy-Littlewood-Sobolev inequality; logarithmic Hardy- Littlewood-Sobolev inequality; Sobolev’s inequality; Onofri’s inequality; Gagliardo-Nirenberg in-

In particular, we want to emphasize that Stochastic Analysis provides nat- ural tools to derive local estimates in the sense that the gradient bound at given point depends only

We are not able to prove such a strong estimate, but we are still able to derive estimate for M(x) from estimates for ψ(x) − x. Our process can be seen as a generalization of

In this paper we use methods from Stochastic Analysis to establish Li-Yau type estimates for positive solutions of the heat equation.. In particular, we want to emphasize

Keywords: Gagliardo–Nirenberg–Sobolev inequalities; Improved inequalities; Manifold of optimal functions; Entropy–entropy production method; Fast diffusion equation;

In particular, for every E every A-harmonicfunction is continuous and Harnack inequalities hold for positive 1-t-harmonic function on every domain in X... Keuntje [Keu90]

The object of this paper is the uniqueness for a d -dimensional Fokker-Planck type equation with inhomogeneous (possibly degenerated) measurable not necessarily bounded