Trends to equilibrium in total variation distance

In Section 3, we present the proof of Theorem 1.2, and as an application, we explain how to use the parabolic Kozono-Taniuchi inequality in order to prove the long time existence

We show that this operator ∇ n plays a key role in a new Poincar´ e (spectral gap) inequality with respect to binomial weights, with the orthogonal Krawtchouk polynomials acting

• if the Poincar´e inequality does not hold, but a weak Poincar´e inequality holds, a weak log-Sobolev inequality also holds (see [12] Proposition 3.1 for the exact relationship

The weak Harnack inequality from our main theorem and the techniques we develop to establish it are deeply rooted in the large literature about elliptic and parabolic regularity,

After that, the main idea consists in proving that the Lagrange multipliers are all zero and that the nodal domains have all the same length (see Section 4).. Existence of a

Of course under stronger assumptions than the sole Poincar´e inequality (logarithmic Sobolev inequality for instance), one can improve the bounds obtained in Theorem 1.1.. Extension

To get the converse, namely to get a counterpart of Gromov-Milman Theorem for convex sets (that the convex Poincar´e inequalities (6.5) or (6.6) imply the dimension free

We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincar´e inequality (for instance logarithmic Sobolev or F -Sobolev).. The case