We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is “almost” characterized by wavelet expansions in the following sense: if a function f is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-`1 type estimates. These weak estimates can be empl...

We study a one-dimensional model describing the motion of a shape-memory alloy spring at a small characteristic time scale, called here fast-temperature-activation limit. At this level, the standard Falk’s model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded weak solution and approximate this nume...

A classical result of Aleksandrov asserts that convex functions in Rn are twice differentiable a.e., and a rst step to prove it is to show that these functions have second order distributional derivatives which are measures, see [4, pp. 239-245]. On the Heisenberg group, and more generally in Carnot groups, several notions of convexity have been introduced and compared in [3] and [7], and Ambro...

This paper is devoted to the global existence of weak solutions three-dimensional compressible Navier--Stokes equations with heat-conducting effects in a bounded domain. The viscosity and heat conductivity coefficients are assumed be functions temperature, shear coefficient may vanish as temperature goes zero. proof apply Galerkin method suitable approximate system several parameters obtain uni...

We give an overview of variational formulations of second-order linear elliptic PDEs that are based on integration by parts (or, equivalently, on Green’s identities).

In this paper we give conditions for the L2-boundedness of singular integrals and the weak type (1,1) of approximate identities on spaces of homogeneous type. Our main tools are Cotlar's lemma and an extension of a theorem of Z6. Introduction. The behavior of singular integrals and approximate identities as operators on the space of integrable functions, i.e. the weak type (1,1), can be investi...

This paper gives a proof of convergence for the approximate solution of an elliptic-hyperbolic system, describing the conservation of two immiscible incompressible phases flowing in a porous medium. The approximate solution is obtained by a mixed finite element method on a large class of meshes for the elliptic equation and a finite volume method for the hyperbolic equation. Since the considere...

Let K be an algebraically closed field of characteristic zero and let I = (f1, . . . , fn) be a homogeneous R+-primary ideal in R := K[X, Y, Z]. If the corresponding syzygy bundle Syz(f1, . . . , fn) on the projective plane is semistable, we show that the Artinian algebra R/I has the Weak Lefschetz property if and only if the syzygy bundle has a special generic splitting type. As a corollary we...

Universal cycles are generalizations of de Bruijn cycles and Gray codes that were introduced originally by Chung, Diaconis, and Graham in 1992. They have been developed by many authors since, for various combinatorial objects such as strings, subsets, permutations, partitions, vector spaces, and designs. One generalization of universal cycles, which require almost complete overlap of consecutiv...