A sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz-Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces

Estimates for solutions to homogeneous Dirichlet problems for a class of elliptic equations with zero order term in the form L(u) = g(x, u) + f (x),where the operator L fulfills an anisotropic elliptic condition, are established. Such estimates are obtained in terms of solutions to suitable problems with radially symmetric data, when no sign conditions on g are required.

A comparison between first-order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number N of pedestrians. The novelty is the fact of considering massive agents, namely, particles whose individual mass does not become infinitesimal when N grows. This implies that the total mass of the system is not constant but grows with N. The main result is that the two types of models approach one another in the limit N -> ?, provided the strength and/or the domain of pedestrian interactions are properly modulated by N at either scale.

In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387-1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm.

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data.

This paper proposes a crowd dynamic macroscopic model grounded on microscopic phenomenological observations which are upscaled by means of a formal mathematical procedure. The actual applicability of the model to real-world problems is tested by considering the pedestrian traffic along footbridges, of interest for Structural and Transportation Engineering. The genuinely macroscopic quantitative description of the crowd flow directly matches the engineering need of bulk results.

We present the latest version of OpenCAPWAP, our open-source implementation of the Internet Engineering Task Force control and provisioning of wireless access point (CAPWAP) protocol. The CAPWAP protocol is designed to support centralized management of large-scale and heterogeneous wireless networks, with a special focus on IEEE 802.11-based networks. The implementation presented in this paper improves substantially on the previous version, adding full support for the Split MAC architecture and decoupling completely the implementation from a specific driver solution.