We study, by means of Γ-convergence, the asymptotic behaviour of a variational problem modeling a dislocation ensemble moving on a slip plane through a discrete array of obstacles. The variational problem is a two dimensional phase transition type energy given by a non local term and a non linear potential which penalizes non integer values. In this paper we consider a regime corresponding to a...

Let T be a k-regular tree (k ≥ 3) and A = Aut(T) its automorphism group. We analyze a generic finitely generated subgroup Γ of A. We show that Γ is free and establish a trichotomy on the closure Γ of Γ in A. It turns out that Γ is either discrete, compact or has index at most 2 in A.

In this paper we consider Γ → M̃ → M , a Galois covering with boundary and D̃/, a Γ-invariant generalized Dirac operator on M̃ . We assume that the group Γ is of polynomial growth with respect to a word metric. By employing the notion of noncommutative spectral section associated to the boundary operator D̃/0 and the b-calculus on Galois coverings with boundary, we develop a higher Atiyah-PatodiSin...

This note completely resolves the asymptotic development of order 2 by Γ-convergence of the mass-constrained Cahn–Hilliard functional, by showing that one of the critical assumptions of the authors’ previous work [10] is unnecessary.

Γ-convergence results for power-law functionals with variable exponents are obtained. The main motivation comes from the study of (first-failure) dielectric breakdown. Some connections with the generalization of the ∞-Laplace equation to the variable exponent setting are also explored. 2000 Mathematics Subject Classification:

We study variational problems with volume constraints (also called level set constraints) of the form

We consider a thin curved film made of a martensitic material. The behavior of the film is governed by a free energy composed of a bulk energy term and an interfacial energy term. We show that the minimizers of the free energy converge to the minimizers of an energy depending on a two-dimensional deformation and one Cosserat vector field when the thickness of the curved film goes to zero. using...

For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ-convergence theorem and show compactness up to translation in all L and certain Orlicz spaces for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher [1] for the coercive two-well case. The theorem has applications to a certain thin-f...

We provide a rigorous justification of the classical linearization approach in plasticity. By taking the small-deformations limit, we prove via Γ-convergence for rate-independent processes that energetic solutions of the quasi-static finite-strain elastoplasticity system converge to the unique strong solution of linearized elastoplasticity.

Let Γ be a finitely presentable pro-p group such that def(Γ) > 0. If Γ has a nontrivial finitely generated closed normal subgroup N of infinite index then def(Γ) = 1, N is a free pro-p group and Γ/N is virtually free. If π is a finitely presentable group with β (2) 1 (π) = 0 then def(π) ≤ 1, with equality only if c.d.π = 2 or π ∼= Z. (See Theorem 2.5 of [1].) The L-Betti number condition holds ...