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 ...

Inverse Compton (IC) scattering of nuclear photons with relativistic electrons in the lobes of powerful radio galaxies and quasars can give detectable extended X–ray emission from the radio lobes if relativistic electrons with a Lorentz factor γ < 300 are present (Brunetti, Setti, Comastri 1997). In general these electrons are not detected since they emit synchrotron radiation at frequencies be...

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)...