The goal of this paper is to extend Poincaré-Wirtinger inequalities from Sobolev spaces to spaces of functions of bounded variation of second order.

We consider a time discrete kinetic scheme (known as “transport collapse method”) for the inviscid Burgers equation ∂tu+ ∂x u 2 = 0. We prove the convergence of the scheme by using averaging lemmas without bounded variation estimate. Then, the extension of this result to the kinetic model of Brenier and Corrias is discussed.

Aim of this note is to provide a brief outline of the theory of shift-differentials, introduced in [2], and show how their construction can be extended to the case of vector valued functions. In the following, we consider the space BV of scalar integrable functions having bounded variation, endowed with the L norm. We recall that, given a map Φ : X 7→ Y between normed linear spaces, its differe...

Multiple-scale homogenization problems are treated in the space BV of functions of bounded variation, using the notion of multiple-scale convergence developed in [35]. In the case of one microscale Amar’s result [3] is recovered under more general conditions; for two or more microscales new results are obtained. AMS Classification Numbers (2010): 49J45, 35B27, 26A45

We present a very short derivation of the integral representation of the two-sided Skorokhod reflection Z of a continuous function X of bounded variation, which is a generalization of the integral representation of the one-sided map featured in [1, 4]. We also show that Z satisfies a simpler integral representation when additional conditions are imposed on X.

We study the asymptotics of subset counts for the uniformly random partition of the set [n]. It is known that typically most of the subsets of the random partition are of size r, with re=n. Confirming a conjecture formulated by Arratia and Tavare , we prove that the counts of other subsets are close, in terms of the total variation distance, to the corresponding segments of a sequence [Zj] of i...

It is obvious that lp (/> 2:1) or any Hubert space satisfies (A). In §3 it is shown that Lp (p>l) does likewise. The method of proof is entirely different from that of Clarkson. In §4 it is shown that if X is any Banach space having the property that every function on a linear interval to X, which satisfies a Lipschitz condition, is differentiable almost everywhere, then also every function of ...

The double Fourier series of functions of the generalized bounded variation class {n/ ln(n + 1)}∗BV are shown to be Pringsheim convergent everywhere. In a certain sense, this result cannot be improved. In general, functions of class Λ∗BV, defined here, have quadrant limits at every point and, for f ∈ Λ∗BV, there exist at most countable sets P and Q such that, for x / ∈ P and y / ∈ Q, f is conti...