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## Publications

Publications (20)

We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong $L^1$-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any...

We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of deterministic particle approximation of partial differential equations. In particular, we provide a $\Gamma$-convergence r...

We consider a one-dimensional aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions.
We prove that the fully deterministic particle approximations with piecewise constant densities introduced in [25] starting from general bounded initial densities converg...

We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general assumptions that the existing literature: the velocity fields are less regular (in particular the interaction...

We present a classification of strict limits of planar BV homeomorphisms. The authors and S. Hencl showed in a previous work \cite{CHKR} that such mappings allow for cavitations and fractures singularities but fulfill a suitable generalization of the INV condition. As pointed out by J. Ball \cite{B}, these features are physically expected by limit...

In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous one-to-one functions on grids. A deep simplification of this property is to consider curves instead of grids, so consid...

We consider an aggregation-diffusion equation, which is the gradient flow in the Wasserstein space of a functional with competing attractive-repulsive interactions. We prove that the fully deterministic particle approximations introduced in \cite{DiFrancesco-Rosini} starting from general bounded initial densities converge to bounded weak solutions...

The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects...

In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous one-to-one functions on the grids. A deep simplification of this property is to consider curves instead of grids, so co...

We propose an ODE-based derivation for a generalized class of opinion formation models either for single and multiple species (followers, leaders, trolls). The approach is purely deterministic and the evolution of the single opinion is determined by the competition between two mechanisms: the opinion diffusion and the compromise process. Such deter...

The fermionic projector state is a distinguished quasi-free state for the algebra of Dirac fields in a globally hyperbolic spacetime. We construct and analyze it in the four-dimensional de Sitter spacetime, both in the closed and in the flat slicing. In the latter case we show that the mass oscillation properties do not hold due to boundary effects...

We show that a planar BV homeomorphism can be approximated in the area strict sense, together with its inverse, with smooth or piecewise affine homeomorphisms.

Given a continuous, injective function j defined on the boundary of a planar open set W, we consider the problem of minimizing the total variation among all the BV homeomorphisms on W coinciding with j on the boundary. We find the explicit value of this infimum in the model case when W is a rectangle. We also present two important consequences of t...

We introduce a new class of planar mappings that allows for cavitations and fractures. The class is the set of strict limits of planar BV homeomorphisms. Each mapping from this class has a proper pointwise representative which is a multifunction, we show that it maps disjoint sets to essentially disjoint sets and that they have an inverse as a prop...

We investigate the existence of weak type solutions for a class of aggregation-diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to nonnegativ...

We construct a deterministic, Lagrangian many-particle approximation to a class of nonlocal transport PDEs with nonlinear mobility arising in many contexts in biology and social sciences. The approximating particle system is a nonlocal version of the follow-the-leader scheme. We rigorously prove that a suitable discrete piece-wise density reconstru...

This Thesis is devoted to the problem of � finding regular approximations of planar homeomorphisms with respect to several suitable distances having important applications in nonlinear elasticity. By regular approximations we intend either di� ffeomorphisms or piecewise a� ne homeomorphisms. Both the results would be interesting in di� fferent cont...

We prove that a planar piecewise affine homeomorphism phi defined on the boundary of the square can be extended to a piecewise affine homeomorphism h of the whole square, in such a way that parallel to h parallel to(W1),(p) is bounded from above by parallel to phi parallel to(W1, p) for every p >= 1.

In this paper we deal with the task of uniformly approximating an L-biLipschitz curve by means of piecewise linear ones. This is rather simple if one is satisfied to have approximating functions which are L′-biLipschitz, for instance this was already done with L′=4L in DP, Lemma 5.5. The main result of this paper is to do the same with L′=L+ε (whic...