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Riesz fractional gradient functionals defined on partitions: nonlocal-to-local variational limits
Stefano Almi, Maicol Caponi, Manuel Friedrich +1
This paper addresses the asymptotics of functionals with linear growth depending on the Riesz -fractional gradient on piecewise constant functions. We consider a general class o…
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…
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 -limit of discrete dislocation fractional energies, without the introduction of a core-radius. By using the finite horiz…
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…
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 -distance of a possibly incomp…
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…