This paper is devoted to prove a continuity theorem for integral functional defined on BV(Ω). This result is applied in order to obtain new relaxation and Γ-convergence theorems on BV(Ω) without any coerciveness and any continuity assumption of the integrand with respect to the spatial variable.

this discrete model can be approximated by a continuous energy defined on special functions with bounded variation. In fact, if we limit the interactions in the sum to the nearest neighbors in the portion of εZ contained in some fixed Ω, and we interpret the values ui as the discretization of a function defined in Ω, then these energies can be studied using the methods of Γ-convergence, and the...

We study the asymptotic behavior of functionals associated to the energy of a thin nonlinear elastic spherical shell in the limit of vanishing thickness (proportional to a small parameter) ε and under the assumption of radial deformations. The functionals are characterized by the presence of a nonlocal potential term and defined on suitable weighted functional spaces. The transition shell-membr...

In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the singlemultiplicity property of the limiting energy, that the Morse indic...

We present the second of two articles on the small volume-fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. After having established the results for the sharp-interface version of the functional [SIAM J. Math. Anal., 42 (2010), pp. 1334–1370], we consider here the full diffuse-interface functional and address the limit in whic...

The Gromov-Lawson-Rosenberg (GLR)-conjecture for a group Γ states that a closed spin manifold M (n ≥ 5) with fundamental group Γ admits a metric with scal > 0 if and only if its C-index α(M) ∈ KOn(C ∗ red (Γ)) vanishes. We prove this for groups Γ with lowdimensional classifying space and products of such groups with free abelian groups, provided the assembly map for the group Γ is (split) injec...

Quantitative description of the statistics of intensity fluctuations within spectral line data cubes introduced in our earlier work is extended to the absorbing media. A possibility of extracting 3D velocity and density statistics from both integrated line intensity as well as from the individual channel maps is analyzed. We find that absorption enables the velocity effects to be seen even if t...

Poly-γ-glutamic acid (γ-PGA), naturally secreted from various strains of Bacillus, has anti-inflammatory activity. In inflammatory bowel disease (IBD), inflammation is promoted and sustained by angiogenesis; however, the role played by γ-PGA in this condition is unclear. Therefore, we evaluated γ-PGA effects on angiogenesis and inflammation in a dextran sulfate sodium-(DSS-) induced mouse colit...

Objective(s):Our recent report indicates that breviscapine play a protective role of the kidney by down-regulating transforming growth factor-β1(TGF-β1), α-smooth muscle actin (α-SMA) and alleviating interstitial fibrosis following unilateral ureteral obstruction (UUO). In this study, we investigate the effect of breviscapine on changes of renal water and sodium transport proteins in response t...