Piecewise constant Mumford-Shah segmentation [17] has been rediscovered by Chan and Vese [6] in the context of region based active contours. The work of Chan and Vese demonstrated many practical applications thanks to their clever numerical implementation using the level-set technology of Osher and Sethian [18]. The current work proposes a Γ -convergence formulation to the piecewise constant Mu...

We study the thin-shell limit of the nonlinear elasticity model for vesicles introduced in part I. We consider vesicles of width 2ε ↓ 0 with elastic energy of order ε 3. In this regime, we show that the limit model is a bending theory for generalized hypersurfaces — namely, co-dimension 1 oriented varifolds without boundary. Up to a positive factor, the limit functional is the Willmore energy. ...

The notion of Wardrop equilibrium in congested networks has been very popular in congested traffic modelling since its introduction in the early 50’s, it is also well-known that Wardrop equilibria may be obtained by some convex minimization problem. In this paper, in the framework of Γ-convergence theory, we analyze what happens when a cartesian network becomes very dense. The continuous model ...

In this paper, we establish the convergence of the Ohta–Kawasaki equation to motion by nonlocal Mullins–Sekerka law on any smooth domain in space dimensions N ≤ 3. These equations arise in modeling microphase separation in diblock copolymers. The only assumptions that guarantee our convergence result are (i) well-preparedness of the initial data and (ii) smoothness of the limiting interface. Ou...

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.