A homogenization problem arising in the gradient theory of fluid-fluid phase transitions is addressed in the vector-valued setting by means of Γ-convergence.

We give a Γ-convergence result for vector-valued nonlinear energies defined on periodically perforated domains. We consider integrands with n-growth where n is the space dimension, showing that there exists a critical scale for the perforations such that the Γ-limit is non-trivial. We prove that the limit extra-term is given by a formula of homogenization type, which simplifies in the case of n...

Γ-convergence techniques are used to give a characterization of the behavior of a family of heterogeneous multiple scale integral functionals. Periodicity, standard growth conditions and nonconvexity are assumed whereas a stronger uniform continuity with respect to the macroscopic variable, normally required in the existing literature, is avoided. An application to dimension reduction problems ...

We consider the problem of the optimal location of a Dirichlet region in a d-dimensional domain Ω subjected to a given force f in order to minimize a given functional. We look for the optimal region among the class of all closed connected sets of assigned total length l. Then we let l tends to infinity and we look at the Γ-limit of a suitable rescaled functional, in order to get information of ...

We fix a finitely presented group Q and consider short exact sequences 1 → N → Γ → Q → 1 with Γ finitely generated. The inclusion N ↪→ Γ induces a morphism of profinite completions N̂ → Γ̂. We prove that this is an isomorphism for all N and Γ if and only if Q is super-perfect and has no proper subgroups of finite index. We prove that there is no algorithm that, given a finitely presented, residua...

In all spatial dimensions d, we study the static and dynamical properties of a generalized Smoluchowski equation which describes the evolution of a gas obeying a logotropic equation of state, p = A ln ρ. A logotrope can be viewed as a limiting form of polytrope (p = Kρ γ , γ = 1 + 1/n), with index γ = 0 or n = −1. In the language of generalized thermodynamics, it corresponds to a Tsallis distri...

We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Γ-convergence arguments. As further developments we consider obstacles with random sizes and shapes located on points of standard lattices, and the case of random homothetics obstacles centered on random Delone sets of points. Obstacle problems for non-local en...

In this paper, a class of minimization problems, labeled by an index 0 < h < 1, is considered. Each minimization problem is for a freeenergy, motivated by the magnetics in 3D-ferromagnetic thin film, and in the context, the index h denotes the thickness of the observing film. The Main Theorem consists of two themes, which are concerned with the study of the solvability (existence of minimizers)...