Day of seminar talks in analysis

by Alan Pinoy (ULB), Anastasia Molchanova (Vienna), Hidde Schönberger (UCLouvain), Stefano Almi (Naples)

Friday 17 Apr 2026, 10:00 → 17:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

10h00-11h00  Stefano Almi (Naples) : Nonlocal approximation of a Griffith-type energy
Abstract: We prove that De Giorgi`s conjecture for nonlocal approximation of free discontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. For a suitable class of continuous finite difference functionals, we show the compactness of deformations with equibounded energies, as well as their Gamma convergence. The compactness (and closure) analysis builds on a Fréchet-Kolmogorov approach and a novel characterization of GSBD.

 

11h15-12h15 Anastasia Molchanova (Vienna) : Hyperelastic Capacitor: A Mixed Lagrangian-Eulerian Variational Model
Abstract: This work investigates the interplay between elastic deformations and electrostatic capacitance in charged elastic materials. We introduce a variational model where the electroelastic energy couples the elastic response with a capacitary term naturally defined in Eulerian coordinates, yielding a mixed Lagrangian-Eulerian energy. We establish the continuity of this capacitary term under suitable convergence of deformations and prove the existence of minimizers in the space of finite‑energy deformations.

12h15-14h30 Lunch break

14h30-15h30 Alan Pinoy (ULB) : A hyperbolic positive mass theorem for asymptotically hyperbolic 3-manifolds via Potential theory
Abstract: In this talk, we will consider some complete non-compact Riemannian manifolds whose geometry near infinity is strongly constrained and resembles that of a fixed model (the euclidean space or the hyperbolic space). These manifolds naturally arise in a variety of areas in geometric analysis and in mathematical relativity. We will define and motivate a geometric invariant, the mass, that quantifies the default for those manifolds to be close the the model. Utilising the Green function for the Laplacian, we will then study this invariant, and answer the following question: can we deform the model in such a way that it does not decrease the curvature?

15h30-16h00 Coffee break

 

16.00h-17.00h Hidde Schönberger (UCLouvain) : Homogenization of nonlocal exchange energies in micromagnetics

Abstract: We study the homogenization of nonlocal micromagnetic functionals incorporating both symmetric and antisymmetric exchange contributions under the physical constraint that the magnetization field takes values in the unit sphere. Assuming that the nonlocal interaction range and the scale of heterogeneities vanish simultaneously, we capture the asymptotic behavior of the nonlocal energies by identifying their Γ-limit, leading to an effective local functional expressed through a tangentially constrained nonlocal cell problem. A main ingredient for the proof is a new characterization of two-scale limits of nonlocal difference quotients, yielding a nonlocal analog of the classical limit decomposition result for gradient fields. To deal with the manifold constraint of the magnetization, we additionally prove that the microscopic oscillations in the two-scale limit are constrained to lie in the tangent space of the sphere.

Based on a joint work with Rossella Giorgio (TU Wien) and Leon Happ (U. Autónoma de Madrid)