Antonio DeSimone

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We examine the singularly perturbed variational problem E ( ) = R 1(1 jr j2)2+ jrr j2 in the plane. As ! 0 this functional favors jr j = 1 and penalizes singularities where jrr j concentrates. Our main result is a compactness theorem: if E ( ) is uniformly bounded then r is compact in L 2. Thus, in the limit ! 0 solves the eikonal equation jr j = 1 almost(More)
High-speed packet networks will begin to support services that need Quality-of-Service (QoS) guarantees. Guaranteeing QoS typically translates to reserving resources for the duration of a call. We propose a state-dependent routing scheme that builds on any base state-independent routing scheme, by routing flows which are blocked on their primary paths (as(More)
We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate(More)
In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The(More)