Geometric implications of the Poincaré inequality

On the Extremal Functions of Sobolev-poincaré Inequality

where ua = 1 vol(Mn) ∫ Mn u, p∗ = np/(n − p) is the Sobolev conjugate of p. This inequality can be proved by combining Sobolev inequality with Poincaré inequality, see, for example, Hebey’s book [8]. In this paper we are interested in the estimates of the best constant and the existence of extremal functions to the above inequality. Analytically these are naturally motivated questions. On the o...

Improved logarithmic-geometric mean inequality and its application

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

Self-improving Properties of Generalized Poincaré Type Inequalities through Rearrangements

We prove, within the context of spaces of homogeneous type, L and exponential type selfimproving properties for measurable functions satisfying the following Poincaré type inequality: inf α ( (f − α)χB )∗ μ ( λμ(B) ) ≤ cλa(B). Here, f ∗ μ denotes the non-increasing rearrangement of f , and a is a functional acting on balls B, satisfying appropriate geometric conditions. Our main result improves...

From the Brunn-Minkowski inequality to a class of Poincaré type inequalities

We present an argument which leads from the Brunn-Minkowski inequality to a Poincaré type inequality on the boundary of a convex body K of class C + in R . We prove that for every ψ ∈ C(∂K)

A REFINEMENT OF THE POINCARÉ INEQUALITY FOR KOLMOGOROV OPERATORS ON Rd