Stefano Almi

Scaling limits for Moran processes on metric strategy spaces: an Eulerian derivation of pure replicator and Fleming--Viot measure-valued PDEs

Stefano Almi, Riccardo Durastanti, Marco Morandotti +2

We study the large-population limit of a discrete-time Moran process featuring multiple strategies, drawn from a possibly infinite strategy space $V$ (a metric space), un…

A Lagrangian superposition principle for the continuity equation with reaction

Stefano Almi, Giacomo Enrico Sodini

We study the continuity equation with reaction $\partial_{t} μ + div (v μ) = w μ$ on $[0, T] \times R^{d}$ , driven by Borel velocity and reaction fields $v$ and $w$ . We…

Approximation of symmetric total variation on point clouds

Stefano Almi, Anna Kubin, Emanuele Tasso

The paper investigates the approximation of the symmetric Total Variation functional on graphs. Such an approximation is given in terms of a discrete and symmetric finite differenc…

Asymptotic analysis for heterogeneous elastic energies with material voids

Stefano Almi, Antonio Flavio Donnarumma, Manuel Friedrich

We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals…

math.AP2025

Gradient regularity for double-phase orthotropic functionals

Stefano Almi, Chiara Leone, Gianluigi Manzo

We prove higher integrability for local minimizers of the double-phase orthotropic functional \[ \sum_{i=1}^{n}\int_Ω\left(\left|u_{x_i}\right|^p+a(x)\left| u_{x_i}\right|^q\right)…

math.AP2025

The superposition principle for the continuity equation with singular flux

Stefano Almi, Riccarda Rossi, Giuseppe Savaré

Representation results for absolutely continuous curves $μ : [0, T] \to P_{p} (R^{d})$ , $p > 1$ , with values in the Wasserstein space $(P_{p} (R^{d}), W_{p})$ of…

math.AP2025

Mean field first order optimality condition under low regularity of controls

Stefano Almi, Riccardo Durastanti, Francesco Solombrino

We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is o…

math.AP2024

On De Giorgi's Conjecture of Nonlocal approximations for free-discontinuity problems: The symmetric gradient case

Stefano Almi, Elisa Davoli, Anna Kubin +1

We prove that E. De Giorgi's conjecture for the nonlocal approximation of free-discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient…

math.AP2024

Thermo-elastodynamics of nonlinearly viscous solids

S. Almi, R. Badal, M. Friedrich +1

In this paper, we study the thermo-elastodynamics of nonlinearly viscous solids in the Kelvin-Voigt rheology where both the elastic and the viscous stress tensors comply with the f…

math.AP2024★ 1 cited

A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations

Stefano Almi, Maicol Caponi, Manuel Friedrich +1

We derive a strain-gradient theory for plasticity as the $Γ$ -limit of discrete dislocation fractional energies, without the introduction of a core-radius. By using the finite horiz…

math.AP2024★ 1 cited

A Pontryagin Maximum Principle for agent-based models with convex state space

Stefano Almi, Riccardo Durastanti, Francesco Solombrino

We derive a first order optimality condition for a class of agent-based systems, as well as for their mean-field counterpart. A relevant difficulty of our analysis is that the stat…

math.AP2024

Linearization in magnetoelasticity

Stefano Almi, Martin Kružík, Anastasia Molchanova

Starting from a model of nonlinear magnetoelasticity where magnetization is defined in the Eulerian configuration while elastic deformation is in the Lagrangean one, we rigorously…

Geometric rigidity for incompatible fields in the multi-well case and an application to strain-gradient plasticity

Stefano Almi, Dario Reggiani, Francesco Solombrino

We derive a quantitative rigidity estimate for a multi-well problem in nonlinear elasticity with dislocations. Precisely, we show that the $L^{1^{*}}$ -distance of a possibly incomp…

A new example for the Lavrentiev phenomenon in Nonlinear Elasticity

Stefano Almi, Stefan Krömer, Anastasia Molchanova

We present a new example for the Lavrentiev phenomenon in context of nonlinear elasticity, caused by an interplay of the elastic energy's resistance to infinite compression and the…

Phase-field topology optimization with periodic microstructure

Stefano Almi, Ulisse Stefanelli

Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealt…

math.AP2023★ 3 cited

Geometric rigidity on Sobolev spaces with variable exponent and applications

Stefano Almi, Maicol Caponi, Manuel Friedrich +1

We present extensions of rigidity estimates and of Korn's inequality to the setting of (mixed) variable exponents growth. The proof techniques, based on a classical covering argume…

Generalized bounded deformation in non-Euclidean settings

Stefano Almi, Emanuele Tasso

We introduce a new space of generalized functions of bounded deformation $GB D_{F}$ , made of functions u whose one-dimensional slice $u (γ) \cdot γ ˙$ has bounded variation in a ge…

Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth

Stefano Almi, Dario Reggiani, Francesco Solombrino

A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided. Our analysis is based on a non-t…

A general criterion for jump set slicing and applications

Stefano Almi, Emanuele Tasso

In this paper a novel criterion for the slicing of the jump set of a function is provided, which bypasses the codimension-one and the parallelogram law techniques developed in $B D$ …

Mean-field limits for entropic multi-population dynamical systems

Stefano Almi, Claudio D'Eramo, Marco Morandotti +1

The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set…

Non-interpenetration conditions in the passage from nonlinear to linearized Griffith fracture

Stefano Almi, Elisa Davoli, Manuel Friedrich

We characterize the passage from nonlinear to linearized Griffith-fracture theories under non-interpenetration constraints. In particular, sequences of deformations satisfying a Ci…