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.

The sedimentation process in an active suspension is the result of the competition between gravity and the autonomous motion of particles. We carry out simulations of run-and-tumble squirmers that move in a fluid medium, focusing on the dependence of the non-equilibrium steady state on the swimming properties.

In this paper we establish the boundedness and the higher differentiability of solutions to the {div(A(x,Du))+b(x)|u(x)|u(x)=fin ?u=0on ?? under a Sobolev assumption on the partial map x->A(x,?). The novelty here is that we deal with degenerate elliptic operator A(x,?) with p-growth, p>=2, with respect to the gradient variable, in presence of lower order terms. The interplay between b(x) and f(x), introduced in ([1]), gives a regularizing effect also in the degenerate elliptic setting.

Skin lesion segmentation is one of the crucial steps for an efficient non-invasive computer-aided early diagnosis of melanoma. This paper investigates how to use colour information, besides saliency, for determining the pigmented lesion region automatically.

GPU version of AMG preconditioner

This paper aims at building a variational approach to the dynamics of discrete topological singularities in two dimensions, based on I"-convergence. We consider discrete systems, described by scalar functions defined on a square lattice and governed by periodic interaction potentials. Our main motivation comes from XY spin systems, described by the phase parameter, and screw dislocations, described by the displacement function. For these systems, we introduce a discrete notion of vorticity.

We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle $\theta$. The ratio between deterministic and stochastic rupture times, though, decreases with $\theta$.

In multitemporal interferometric synthetic aperture radar (InSAR) applications, propagation delay in the troposphere introduces a major source of disturbance known as atmospheric phase screen (APS). This study proposes a novel framework to compensate for the APS from multitemporal ground-based InSAR data. The proposed framework first performs time-series clustering in accordance with the temporal APS behavior realized by the k-means clustering approach. In the second step, joint estimation of the APS and displacement velocity is performed.

We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

Stabilized dense emulsions display a rich phenomenology connecting microstructure and rheology. In this work we study how an emulsion with a finite yield stress can be built via large-scale stirring. By gradually increasing the volume fraction of the dispersed minority phase, under the constant action of a stirring force, we are able to achieve volume fractions close to 80%. Despite the fact that our system is highly concentrated and not yet turbulent we observe a droplet size distribution consistent with the -10/3 scaling, often associated to inertial range droplets breakup.