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Generalised functions of bounded deformation

Gianni Dal Maso (2013)

Journal of the European Mathematical Society

We introduce the space G B D of generalized functions of bounded deformation and study the structure properties of these functions: the rectiability and the slicing properties of their jump sets, and the existence of their approximate symmetric gradients. We conclude by proving a compactness results for G B D , which leads to a compactness result for the space G S B D of generalized special functions of bounded deformation. The latter is connected to the existence of solutions to a weak formulation of some variational...

Hilbert-valued forms and barriers on weakly pseudoconvex domains.

Vincent Thilliez (1998)

Publicacions Matemàtiques

We introduce an alternative proof of the existence of certain Ck barrier maps, with polynomial explosion of the derivatives, on weakly pseudoconvex domains in Cn. Barriers of this sort have been constructed very recently by J. Michel and M.-C. Shaw, and have various applications. In our paper, the adaptation of Hörmander's L2 techniques to suitable vector-valued functions allows us to give a very simple approach of the problem and to improve some aspects of the result of Michel and Shaw, regarding...

On a generalization of Nikolskij's extension theorem in the case of two variables

Alexander Ženíšek (2003)

Applications of Mathematics

A modification of the Nikolskij extension theorem for functions from Sobolev spaces H k ( Ω ) is presented. This modification requires the boundary ∂ Ω to be only Lipschitz continuous for an arbitrary k ∈ ℕ ; however, it is restricted to the case of two-dimensional bounded domains.

Quelques curieuses topologies sur M μ ( T ) et M β ( T )

Henri Buchwalter (1977)

Annales de l'institut Fourier

Pour tout compact complètement régulier T , on désigne par M β ( T ) l’espace des mesures de Radon sur le compactifié de Stone-Cech β T de T et par M σ ( T ) son sous-espace formé des mesures σ -régulières au sens de Varadarajan. On décrit alors sur ces deux espaces des topologies T p , 1 ≤ p ≤ + ∞ , qui possèdent des propriétés curieuses parmi lesquelles il convient de citer la suivante : pour 1 < p ≤ + ∞ et pour tout T non pseudocompact, l’espace ( M σ ( T ) , T p ) est non quasi-complet mais ses précompacts sont relativement compacts. Ce résultat permet...

Regulated functions

Dana Fraňková (1991)

Mathematica Bohemica

The first section consists of auxiliary results about nondecreasing real functions. In the second section a new characterization of relatively compact sets of regulated functions in the sup-norm topology is brought, and the third section includes, among others, an analogue of Helly's Choice Theorem in the space of regulated functions.

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