Let I be an open bounded interval of R and W a non-negative continuous function vanishing only at α, β ∈ R. We investigate the asymptotic behaviour in terms of Γ-convergence of the following functional Gε(u) := ε p−2 ∫∫ I×I ∣∣∣∣u(x)− u(y) x− y ∣∣∣∣pdxdy + 1ε ∫ I W (u) dx (p > 2), as ε→ 0. Mathematics Subject Classification (2000). Primary 82B26, 49J45 ; Secondary 49Q20.

We investigate the possibility of describing the “limit problem” of a sequence of optimal control problems (P)(bn), each of which is characterized by the presence of a time dependent vector valued coefficient bn = (bn1 , . . . , bnM ). The notion of “limit problem” is intended in the sense of Γ-convergence, which, roughly speaking, prescribes the convergence of both the minimizers and the infim...

this paper reports results of a study regarding the activities of nano structure mn/γ-al2o3 and γ-al2o3 catalysts for oxidation of 2-propanol (as a model of volatile organic compound). nanostructure of catalysts was revealed using xrd, sem and tem techniques. catalytic studies were carried out in u-shaped packed bed reactor under atmospheric pressure and at the reaction temperature of 150- 500°...

We characterize the relaxation of the perimeter in an infinite dimensional Wiener space, with respect to the weak L-topology. We also show that the rescaled AllenCahn functionals approximate this relaxed functional in the sense of Γ-convergence.

The goal of this paper is to solve a long standing open problem, namely, the asymptotic development of order 2 by Γ-convergence of the mass-constrained Cahn–Hilliard functional. This is achieved by introducing a novel rearrangement technique, which works without Dirichlet boundary conditions.

This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an open crosssection which is the union of rectangles with sides of order ε and ε2, as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the threedimensional problem Γ-converges to the classical one-dimension...

In this paper we consider the asymptotic behavior of the GinzburgLandau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via Γ-convergence, a reduced model for the vortex density, and deduce a curvature equation for the vortex lines. In the companion paper [2] we describe further applications to superconductivity and superfluidity, such as...

A class of free-discontinuity problems is approximated in the sense of Γ-convergence by a sequence of non-local integral functionals.

In this paper, we study nonlocal gradients and their relationship to classical gradients. As the nonlocality vanishes we demonstrate the convergence of nonlocal gradients to their local analogue for Sobolev and BV functions. As a consequence of these localizations we give new characterizations of the Sobolev and BV spaces that are in the same spirit of Bourgain, Brezis, and Mironsecu’s 2001 cha...