Search results for "continuity"

THE MINIMIZING TOTAL VARIATION FLOW WITH MEASURE INITIAL CONDITIONS

2004

In this paper we obtain existence and uniqueness of solutions for the Cauchy problem for the minimizing total variation flow when the initial condition is a Radon measure in ℝN. We study limit solutions obtained by weakly approximating the initial measure μ by functions in L1(ℝN). We are able to characterize limit solutions when the initial condition μ=h+μs, where h∈L1(ℝN)∩L∞(ℝN), and μs=αℋk⌊ S,α≥0,k is an integer and S is a k-dimensional manifold with bounded curvatures. In case k<N-1 we prove that the singular part of the solution does not move, it remains equal to μs for all t≥0. In particular, u(t)=δ0 when u(0)=δ0. In case k=N-1 we prove that the singular part of the limit solution …

Abitare nel reale. Dalla crisi della periferia alla tessitura di nuove relazioni contestuali

2019

I progetti redatti per “Palermo Sud-Est” sono il risultato di un Laboratorio di Laurea strutturatosi attraverso incontri, seminari, comunicazioni specialistiche, esposizioni critiche, che – in una strategia condivisa – ha visto ogni studente elaborare il proprio lavoro nel confronto con gli altri attori del Laboratorio stesso. La ricerca sui “progetti urbani” è stata impostata di modo che ogni laureando fosse messo a conoscenza dei progetti svolti nello stesso ambito territoriale dai colleghi che l’avevano preceduto, così da poter operare in continuità e contribuire a formulare un ragionamento unitario, nel quale ogni progetto costituisse continuazione, verifica o anche variante dei precede…

Multiple odontogenic abscesses. Thoracic and abdomino-perineal extensión in an immuno competent patient

2010

Introduction: Odontogenic infection (OI) may lead to death if it extends beyond the buccal area. The virulence of pathogens and the local and systemic status of the patient influence the propagation of the pathogen, either by anatomical continuity or haemematogenous dissemination. Several severe complications derived from OI have been reported in the head, neck and chest. However, OI with an abdominal component, caused by bacteraemia with dental foci or the direct passage of pus from the thorax to the abdomen, are unusual. Case report: We present the case of a young immunocompetent woman who, after false cure of an odontogenic abscess, again reported gynaecological symptoms. A network of co…

Versus. Quaderni di Studi Semiotici. Gennaio-Giugno 2014.

2014

Menger curvature and Lipschitz parametrizations in metric spaces

2005

Quasihyperbolic boundary conditions and capacity: Uniform continuity of quasiconformal mappings

2005

We prove that quasiconformal maps onto domains which satisfy a suitable growth condition on the quasihyperbolic metric are uniformly continuous when the source domain is equipped with the internal metric. The obtained modulus of continuity and the growth assumption on the quasihyperbolic metric are shown to be essentially sharp. As a tool, we prove a new capacity estimate.

Some Non-linear Geometrical Properties of Banach Spaces

2014

In this survey we report on very recent results about some non-linear geometrical properties of many classes of real and complex Banach spaces and uniform algebras, including the ball algebra \(\fancyscript{A}_u(B_X)\) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space \(X\). These geometrical properties are: Polynomial numerical index, Polynomial Daugavet property and Bishop-Phelp-Bollobas property for multilinear mappings.

On holomorphic functions attaining their norms

2004

Abstract We show that on a complex Banach space X , the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that X has the Radon–Nikodym property. We also show that the same result holds for Banach spaces having a strengthened version of the approximation property but considering just functions which are also weakly uniformly continuous on the unit ball. We prove that there exists a polynomial such that for any fixed positive integer k , it cannot be approximated by norm attaining polynomials with degree less than k . For X=d ∗ (ω,1) , a predual of a Lorentz sequence space, we prove that the product of two p…

Boundary blow-up under Sobolev mappings

2014

We prove that for mappings $W^{1,n}(B^n, \R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.

Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere

2013

Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.