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Federico Stra

Publications and source records attributed to Federico Stra.

13 recordsLinked to original sources
arXiv2026

Minimizers of one-dimensional regularization problems with linear and nonlinear total variation

A study of the minimizers of one-dimensional Rudin-Osher-Fatemi-type functionals with linear or nonlinear total variation and fidelity term is undertaken. Conditions on the input datum and the parameters of the functional are found that force the input itself to be the minimizer or not. In the linear setting the discriminating conditions on the parameters are complementary highlighting the sharpness of the results. The nonlinear setting is substantially different: while the non-minimality of the datum is treated in analogy with the linear case, for the minimality of the input only partial answers are found. The results in the nonlinear setting hinge on auxiliary constrained or penalized minimization problems investigating the behavior of optimal transitions with prescribed height. Additionally, they are complemented by some numerical examples.

math.CA↗
arXiv2026

On the existence of optimizers for nonlinear time-frequency concentration problems: the Born--Jordan distribution

We study the $L^p$ concentration problem for the Born--Jordan distribution in dimension $d>1$, thus extending the one-dimensional analysis in [Stra-Svela-Trapasso, J. Math. Pures Appl. (2026)]. We show that the existence of concentration optimizers depends on the exponent $p$ with a critical threshold at $p_*(d)= \frac{2d}{d-2}$ for $d\geq2$ (with the understanding that $p_*(2)=\infty$). In particular, for subcritical exponents $1\leq p p_*(d)$ we show that the functional is unbounded. We also provide the complete solution in the (significantly more) challenging critical regime in dimension $d=2$.

math.CA↗
arXiv2025

On the existence of optimizers for nonlinear time-frequency concentration problems: the Wigner distribution

We prove that, for any measurable phase space subset $\Omega\subset\mathbb{R}^{2d}$ with $0<|\Omega|<\infty$ and any $1\le p < \infty$, the nonlinear concentration problem $$ \sup_{f \in L^2(\mathbb{R}^d)\setminus\{0\}}\frac{\|Wf\|_{L^p(\Omega)}}{\|f\|_{L^2}^2}$$ admits an optimizer, where $Wf$ is the Wigner distribution of $f$. The main obstruction is that $Wf$ is covariant (not invariant) under time-frequency shifts, which impedes weak upper semicontinuity, so the effects of constructive interference must be taken into account. We close this compactness gap via concentration compactness for Heisenberg-type dislocations, together with a new asymptotic formula that quantifies the limiting contribution to concentration over $\Omega$ from asymptotically separated wave packets. When $p=\infty$ we also identify the sharp constant $2^d$ and show that it is attained. We also discuss some related extensions: For $\tau$-Wigner distributions with $\tau \in (0,1)$ we isolate a chain phenomenon that obstructs the same strategy beyond the Wigner case ($\tau=1/2$), while for the Born-Jordan distribution in $d=1$ we obtain weak continuity, and thus existence of concentration optimizers for all $1\le p<\infty$ (the $p=\infty$ supremum equals $\pi$ but is not attained).

math.CA↗
arXiv2025

Excess-continuous prox-regular sweeping processes

In this paper we consider the Moreau's sweeping processes driven by a time dependent prox-regular set $C(t)$ which is continuous in time with respect to the asymmetric distance $e$ called the excess, defined by $e(A,B) := \sup_{x \in A} d(x,B)$ for every pair of sets $A$, $B$ in a Hilbert space. As observed by J.J. Moreau in his pioneering works, the excess provides the natural topological framework for sweeping process. Assuming a uniform interior cone condition for $C(t)$, we prove that the associated sweeping process has a unique solution, thereby improving the existing result on continuous prox-regular sweeping processes in two directions: indeed, in the previous literature $C(t)$ was supposed to be continuous in time with respect to the symmetric Hausdorff distance instead of the excess and also its boundary $\partial C(t)$ was required to be continuous in time, an assumption which we completely drop. Therefore our result allows to consider a much wider class of continuously moving constraints.

math.CA↗
arXiv2024

Deterministic particle method for nonlinear nonlocal scalar balance equations

We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to "Radici-Stra [SIAM J. Math. Anal. 55.3 (2023)]" is the presence of a source term; this causes the solutions to no longer be probability measures, thus requiring a suitable adaptation of the numerical scheme and of the estimates leading to compactness.

math.AP↗
arXiv2022

Stability of quasi-entropy solutions of non-local scalar conservation laws

We prove the stability of entropy solutions of nonlinear conservation laws with respect to perturbations of the initial datum, the space-time dependent flux and the entropy inequalities. Such a general stability theorem is motivated by the study of problems in which the flux $P[u](t,x,u)$ depends possibly non-locally on the solution itself. For these problems we show the conditional existence and uniqueness of entropy solutions. Moreover, the relaxation of the entropy inequality allows to treat approximate solutions arising from various numerical schemes. This can be used to derive the rate of convergence of the recent particle method introduced in [Radici-Stra 2021] to solve a one-dimensional model of traffic with congestion, as well as recover already known rates for some other approximation methods.

math.AP↗
arXiv2021

Entropy solutions of non-local scalar conservation laws with congestion via deterministic particle method

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 force can have a discontinuity at the origin) with no prescribed attractive/repulsive regime and the mobility can have unbounded support. We complement our results with some numerical simulations, among which we show the applicability of the schemes to the multi-species setting.

math.AP↗
arXiv2020

Lagrangian discretization of crowd motion and linear diffusion

We study a model of crowd motion following a gradient vector field, with possibly additional interaction terms such as attraction/repulsion, and we present a numerical scheme for its solution through a Lagrangian discretization. The density constraint of the resulting particles is enforced by means of a partial optimal transport problem at each time step. We prove the convergence of the discrete measures to a solution of the continuous PDE describing the crowd motion in dimension one. In a second part, we show how a similar approach can be used to construct a Lagrangian discretization of a linear advection-diffusion equation, interpreted as a gradient flow in Wasserstein space. We provide also a numerical implementation in 2D to demonstrate the feasibility of the computations.

math.NA↗
arXiv2016

A PDE approach to a 2-dimensional matching problem

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by S.\ Caracciolo et al.\ (Phys. Rev. E, {\bf 90} 012118, 2014) that "linearise" the Monge-Ampère equation.

math.PR↗
arXiv2016

Weak and strong convergence of derivations and stability of flows with respect to MGH convergence

This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X,d,m_n), m_n weakly convergent to m. In particular, under curvature assumptions, either only on the limit metric structure (X,d,m) or on the whole sequence of metric measure spaces, we provide several stability results.

math.MG↗