A class of structures is said to have the homomorphism-preservation property just in case every firstorder formula that is preserved by homomorphisms on this class is equivalent to an existential-positive formula. It is known by a result of Rossman that the class of finite structures has this property and by previous work of Atserias et al. that various of its subclasses do. We extend the latte...

Recall that a function u is harmonic (superharmonic, subharmonic) in an open set U ⊂ Rn (n ≥ 1) if u ∈ C2(U) and Δu = 0 (Δu ≤ 0,Δu ≥ 0) on U . Denote by H(U) the space of harmonic functions in U and SH(U) (sH(U)) the subset of C2(U) consisting of superharmonic (subharmonic) functions in U . If A ⊂ Rn is Lebesgue measurable, L1(A) denotes the space of Lebesgue integrable functions on A and |A| d...

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...