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Shift inequalities of Gaussian type and norms of barycentres

F. Barthe, D. Cordero-Erausquin, M. Fradelizi (2001)

Studia Mathematica

We derive the equivalence of different forms of Gaussian type shift inequalities. This completes previous results by Bobkov. Our argument strongly relies on the Gaussian model for which we give a geometric approach in terms of norms of barycentres. Similar inequalities hold in the discrete setting; they improve the known results on the so-called isodiametral problem for the discrete cube. The study of norms of barycentres for subsets of convex bodies completes the exposition.

Short-time heat flow and functions of bounded variation in R N

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove a characterisation of sets with finite perimeter and B V functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.

Sierpiński's hierarchy and locally Lipschitz functions

Michał Morayne (1995)

Fundamenta Mathematicae

Let Z be an uncountable Polish space. It is a classical result that if I ⊆ ℝ is any interval (proper or not), f: I → ℝ and α < ω 1 then f ○ g ∈ B α ( Z ) for every g ∈ B α ( Z ) ∩ Z I if and only if f is continuous on I, where B α ( Z ) stands for the αth class in Baire’s classification of Borel measurable functions. We shall prove that for the classes S α ( Z ) ( α > 0 ) in Sierpiński’s classification of Borel measurable functions the analogous result holds where the condition that f is continuous is replaced by the condition that f is locally Lipschitz...

Simmetrizzazione e disuguaglianze di tipo Pòlya-Szegö

Nicola Fusco (2005)

Bollettino dell'Unione Matematica Italiana

Si presentano alcuni risultati recenti riguardanti la disuguaglianza di Pòlya- Szegö e la caratterizzazione dei casi in cui essa si riduce ad un'uguaglianza. Particolare attenzione viene rivolta alla simmetrizzazione di Steiner di insiemi di perimetro finito e di funzioni di Sobolev.

Singular points of order k of Clarke regular and arbitrary functions

Luděk Zajíček (2012)

Commentationes Mathematicae Universitatis Carolinae

Let X be a separable Banach space and f a locally Lipschitz real function on X . For k ∈ ℕ , let Σ k ( f ) be the set of points x ∈ X , at which the Clarke subdifferential ∂ C f ( x ) is at least k -dimensional. It is well-known that if f is convex or semiconvex (semiconcave), then Σ k ( f ) can be covered by countably many Lipschitz surfaces of codimension k . We show that this result holds even for each Clarke regular function (and so also for each approximately convex function). Motivated by a resent result of A.D. Ioffe, we prove...

Singularité réelle isolée

Ahmed Jeddi (1991)

Annales de l'institut Fourier

Soit un germe de fonction analytique f : ( R n + 1 , 0 ) → ( R , 0 ) , n ≥ 1 à singularité isolée en 0 ∈ R n + 1 . Nous nous proposons d’étudier le développement asymptotique des intégrales de formes C c ∞ , de degré n , sur les fibres de f . Nous montrons que ces développements asymptotiques peuvent être décrits à partir de l’action de la monodromie sur le groupe H n de la fibre de Milnor complexe.

Singularities and equicontinuity of certain families of set-valued mappings

Tiberiu Trif (1998)

Commentationes Mathematicae Universitatis Carolinae

In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex processes is derived. This principle immediately yields the uniform boundedness theorem stated in [1, Theorem...

Smooth Cantor functions

T. W. Körner (2007)

Colloquium Mathematicae

We characterise the set on which an infinitely differentiable function can be locally polynomial.

Currently displaying 61 – 80 of 472