il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terrà giovedì 17 ottobre 2024 alle ore 15.30, nella Sala Professori 1° Livello. Di seguito, riportiamo i nomi dei due speaker e gli abstract dei loro talk.

Maicol Caponi: “A fractional approach to strain-gradient plasticity:
beyond core-radius of discrete dislocations”
Abstract: In this talk we derive a strain-gradient theory for plasticity
as the Gamma-limit of discrete dislocation fractional energies, without
the introduction of a core-radius. By using the finite horizon
fractional gradient introduced by Bellido, Cueto, and Mora-Corral, we
consider a nonlocal model of semi-discrete dislocations, in which the
stored elastic energy is computed via the fractional gradient of order
1-alpha. As alpha goes to 0, we show that suitably rescaled energies
Gamma-converge to the macroscopic strain-gradient model of Garroni,
Leoni, and Ponsiglione.
This is a joint work with Stefano Almi (Università degli Studi di Napoli
“Federico II”), Manuel Friedrich (FAU Erlangen-Nürnberg), and Francesco
Solombrino (Università degli Studi di Napoli “Federico”).

Giulio Pascale:  “Variational Results on Capillary Isoperimetric
Problems and Liquid Drop Models”
Abstract: The classical capillarity problem aims at minimizing, among
sets satisfying a volume constraint in a given container, a suitable
weighted perimeter. We consider the  contribution of the interface that
touches the boundary of the container as being weighted by a fixed
constant representing the relative adhesion coefficient between aliquid
drop and the solid walls of the container. If the container is a
halfspace, the isoperimetric sets for such problem are given by suitably
truncated balls lying on the boundary of the halfspace.
The aim of this talk is to present a new quantitative isoperimetric
inequality for the capillarity problem in a halfspace, which estimates
the asymmetry of a competitor relative to the optimal bubble with the
corresponding isoperimetric deficit, together with some existence
results when nonlocal interaction and gravity are added.
The talk is based on an ongoing project in collaboration with M.
Pozzetta.
References:
[1] G.Pascale, M.Pozzetta, Quantitative isoperimetric inequalities for
classical capillarity problems,Calc.Var., 2024.
[2] G.Pascale, Existence and nonexistence of minimizers for classical
capillarity problems in presence of nonlocal repulsion and gravity,
ArXiv, 2024.