In this paper we establish an higher integrability result for second derivatives of the local solution of elliptic equation div(A(x,Du))=0in?where ? ? R, n>= 2 and A(x, ?) has linear growth with respect to ? variable. Concerning the dependence on the x-variable, we shall assume that, for the map x-> A(x, ?) , there exists a non negative function k(x), such that |DxA(x,?)|?k(x)(1+|?|)for every ?? R and a.e. x? ?. It is well known that there exists a relationship between this condition and the regularity of the solutions of the equation.

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We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations.

Invasive species cause huge amounts of environmental, economic, social and cultural damage in Europe and worldwide. Improving measures to control them is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management (1; 2; 4). We analyse an optimal control model for the control of invasive species which aims to find the best temporal resource allocation strategy for the population reduction, under a budget constraint (3).

We present an all-around study of the visitors flow in crowded museums: a combination of Lagrangian field measurements and statistical analyses enable us to create stochastic digital-twins of the guest dynamics, unlocking comfort- and safety-driven optimizations. Our case study is the Galleria Borghese museum in Rome (Italy), in which we performed a real-life data acquisition campaign.

The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradient flow structure of the equation and establish differential and algebraic relationships between the energy, the dissipation, and the squared H -1 distance to a kink.

The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) measured the middle-infrared limb emission spectrum of the atmosphere from 2002 to 2012 on board ENVISAT, a polar-orbiting satellite. Recently, the European Space Agency (ESA) completed the final reprocessing of MIPAS measurements, using version 8 of the level 1 and level 2 processors, which include more accurate models, processing strategies, and auxiliary data. The list of retrieved gases has been extended, and it now includes a number of new species with weak emission features in the MIPAS spectral range.

The diffusive behaviour of simple random-walk proposals of many Markov Chain Monte Carlo (MCMC) algorithms results in slow exploration of the state space making inefficient the convergence to a target distribution. Hamiltonian/Hybrid Monte Carlo (HMC), by introducing fictious momentum variables, adopts Hamiltonian dynamics, rather than a probability distribution, to propose future states in the Markov chain. Splitting schemes are numerical integrators for Hamiltonian problems that may advantageously replace the St¨ormer-Verlet method within HMC methodology.

Terrestrial and marine ecosystems provide essential goods and services to human societies. In the last decades, however, anthropogenic pressure has produced a loss of ecosystem services that can seriously affect human wellbeing and climate processes at local and regional scale.