Nonlinear Analysis and the Physics of Materials

Liste des Contributions

3. Welcome address

01/06/2026 11:10

1. Some known and less known remarks about the Jacobi formula for the Jacobian

Jean Mawhin

01/06/2026 11:15

Petru Mironescu, in a series of works alone or in collaboration, especially with the late Haïm Brezis, has shown the important role played by a formula of Jacobi in the definition and study of the distributional Jacobian.

In this lecture, we recall some aspects of the tortuous history of this formula described in [1], and comment on some new historical facts and some new links to classical...

2. The weak approximation problem for manifold-valued Sobolev mappings

Antoine Detaille

01/06/2026 12:00

In a striking contrast with the classical situation of real-valued Sobolev functions, a Sobolev mapping taking its values into a manifold N need not be a limit of smooth N-valued maps with respect to the strong convergence.
A natural idea to try restoring the approximation property by smooth maps is to work with a weaker notion of convergence.
Unlike the strong approximation problem, which...

5. Extrapolation methods for Γ-convergence and applications to image processing

Oscar Dominguez

01/06/2026 14:15

In this talk, we introduce, via the Gagliardo completion, an extrapolation framework within De Giorgi’s Γ-convergence theory and develop its applications to variational problems arising in image processing, in particular, the Rudin-Osher-Fatemi (ROF) model. Special emphasis is given to new tools connecting extrapolation theory and variational analysis, specifically the extrapolation of...

4. Minimizing N-harmonic maps with partially constrained boundary conditions of prescribed degree

Adriano Pisante

01/06/2026 15:00

In this talk we will focus for $N\geq 2$ on fractional $W^{1-1/N,N}$ maps from an $(N−1)$-dimensional sphere into itself as traces of maps with finite energies modelled on the $N$-Dirichlet integral. We consider energy minimization among maps with trace of prescribed topological degree. Our goal is to prove existence and quantitative stability for minimizers in homotopy classes. Due to the...

6. Point singularities of manifold-valued Sobolev maps and approximability by smooth maps

Giacomo Canevari

01/06/2026 16:15

Manifold-valued Sobolev maps naturally arise in variational problems and models of partially ordered media, where the topology of the target can enforce the formation of singularities. These singularities may act as obstructions to familiar constructions, such as approximation by smooth maps. In this talk, given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of...

8. On CMC 1-immersions of a closed surface into Hyperbolic 3-manifolds

Gabriella Tarantello

02/06/2026 09:15

Constant Mean Curvature (CMC) c-immersions of a closed orientable surface S (with genus g ≥ 2) into hyperbolic 3-manifolds emerged by the work of Uhlenbeck in connection with irreducible representations of the fundamental group of S into the Mobious group.

In view of Bryant surfaces, the value c =1 of the mean curvature enters as a “critical” (yet significant) parameter in this context....

9. Rigidity and flexibility for infinite double bubbles

Mike Novack

02/06/2026 10:00

The classical double bubble theorem characterizes in every dimension surface-area minimizing partitions of R^n into three chambers, two of which have prescribed finite volume. In this talk we will discuss a variant of the double bubble problem in which two of the chambers have infinite volume. Unlike the standard double bubble problem, the characterization of minimizers depends on the...

10. mod(q) area-minimizing surfaces: structure and singularities

Anna Skorobogatova

02/06/2026 11:15

One possible framework in which to study the Plateau problem is by using currents with multiplicities modulo q, for a fixed integer q. This setting allows for minimizing surfaces to exhibit codimension 1 singularities like triple junctions, which are seen in physical soap films, and has close connections to the known regularity theory for stable minimal submanifolds, while at the same time...

11. On Minimizing Harmonic Maps with Tangential Boundary Anchoring

Dominik Stantejsky

02/06/2026 12:00

Motivated by experiments with nematic liquid crystal droplets, we study harmonic maps on the three-dimensional unit ball that arise as minimizers of the one-constant approximation of the Oseen-Frank energy subject to strong anchoring planar boundary condition. Through a reflection method, we are able to study regularity of minimizers close to the boundary. We also obtain results on the type...

12. 3D local minimizers to vector Allen-Cahn converging down to asymmetric tetrahedral cones

Peter Sternberg

02/06/2026 14:30

We consider the vector Allen-Cahn (Modica-Mortola) energy with a 4-well potential. The goal is to produce a stable, diffuse version of a stable, tetrahedral cone in the absence of any symmetry assumptions. This is accomplished via standard Gamma-convergence theory once we can exhibit a bounded 3D domain which is partitioned by such a cone into a locally minimizing 4 chamber configuration with...

13. Minimisers of nonlocal energies: the effect of anisotropy

Lucia Scardia

02/06/2026 15:15

Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels?

I will present some results and partial answers in this direction obtained in...

14. Geometry and Topology of Mappings with Derivatives of Small Rank

Piotr Hajłasz

02/06/2026 16:30

The main theme of this talk is the study of mappings—primarily continuously differentiable and Lipschitz—that are critical everywhere, in the sense that the rank of their derivative is small at every point. Such mappings arise naturally in a variety of contexts across analysis, geometry, and topology. I will show how ideas from different areas combine to address fundamental questions about...

15. A symmetry result related to the baby Skyrme model

Etienne Sandier

03/06/2026 10:00

We show a symmetry result in an exterior domain in dimension 2 for minimizing harmonic maps to the sphere perturbed by a jacobian term. We hope this could be useful in the study of various Skyrmion models.

17. Integrability of the full gradient for Griffith minimizers in dimension 2

Antoine Lemenant

03/06/2026 11:15

The Griffith functional, arising in variational models of crack propagation and linearized elasticity, shares many features with the classical Mumford–Shah functional. A major difficulty in this vectorial setting is that the energy only controls the symmetric part of the gradient, rather than the full gradient itself. In this talk, I will present a strategy to obtain the L^2-integrability of...

18. Another look at Boojums in a Liquid Crystal Model

Itai Shafrir

03/06/2026 12:00

Several authors (Alama, Bronsard, Golovaty, Mironescu) have recently studied
the minimizers $\{u_\varepsilon\}$ of the energy $ E_\varepsilon(u) = E^{g,\alpha}_\varepsilon(u)$, given by
\begin{equation}
%\label{eq:1}
E_\varepsilon(u) = \frac{1}{2} \int_\Omega \left( |\nabla
u|^2 + \frac{1}{2\varepsilon^2}(1 - |u|^2)^2 \right) \, dx + \frac{1}{2\varepsilon^s} \int_{\partial\Omega}
...

29. Conference dinner

03/06/2026 20:00

at Aux Pieds Sous La Table

23. Traces of Sobolev Spaces

Giovanni Leoni

04/06/2026 09:15

This talk explores the trace theory of Sobolev spaces in the critical $p=1$ case. After reviewing the first-order case in which the trace of $W^{1,1}(\Omega)$ is $L^1(\partial\Omega)$, we focus on higher-order Sobolev spaces whose traces are Besov spaces. We will present new and classical results on the trace and lifting problem for these spaces.

20. Phase-field model for polycrystals

Adriana Garroni

04/06/2026 10:00

I will present a recent result obtained in collaboration with S. Conti, V. Crismale and A. Malusa.
We consider a phase-field model `a la Ambrosio Tortorelli in order to approximate sharp interface energies for grain boundaries accounting for the Read and Shockley law for small angle grain boundaries.
The independent variable takes values in the orthogonal group O(d) modulo a lattice point...

21. Quantitative concentration and Wehrl-type entropy inequalities for homogeneous polynomials

Maria Angeles Garcia Ferrero

04/06/2026 11:15

Let us consider two notions of concentration for homogeneous polynomials in d complex variables on the unit sphere: a local notion measuring the fraction of the L2-norm supported on a measurable subset and a global notion given by the generalized Wehrl entropy. Lieb and Solovej proved that the extremizers in both cases are monomials up to a unitary rotation. Their result generalizes the one by...

22. Stochastic homogenization of the double-porosity model

Elise Bonhomme

04/06/2026 12:00

In this talk, I will present joint work with Mitia Duerinckx and Antoine Gloria, in which we establish the homogenization of the so-called "double-porosity" model in a random setting where the resonant inclusions are neither uniformly bounded nor uniformly separated. This mesoscopic model (used to describe flows in fractured porous media) arises as the limit of a diffusion process in a highly...

19. A topological toolbox for Sobolev maps

Augusto Ponce

04/06/2026 14:30

Classical works by F. Bethuel and by F. Hang and F.-H. Lin identified the local and global topological obstructions preventing smooth maps from being dense in the Sobolev space $W^{1,p}(M^{m};N^{n})$ between two Riemannian manifolds when $p<m$. These obstructions are related to the extension of continuous maps from certain subsets of $M^{m}$ into $N^{n}$.

Inspired by the notion of modulus...

24. On s-Stability of W^{s,n/s}-minimizing maps between spheres in homotopy classes

Katarzyna Mazowiecka

04/06/2026 15:15

We consider maps between spheres $\mathbb S^n$ to $\mathbb S^\ell$ that minimize the Sobolev-space energy $W^{s,n/s}$ for some $s \in (0,1)$ in a given homotopy class. The basic question is: in which homotopy class does a minimizer exist? This is a nontrivial question since the energy under consideration is conformally invariant and bubbles can form. Sacks-Uhlenbeck theory tells us that...

30. Existence of critical points of the n-Ginzburg-Landau energy with prescribed degree 1

Rémy Rodiac

04/06/2026 16:30

We will discuss the existence of critical points of the $n$-Ginzburg-Landau energy in the unit ball of $\mathbb R^n$ with prescribed degree one on the boundary. We will first prove that there does not exist any minimizer of this energy among maps with prescribed degree $d\neq 0$. Then we will show that we can devise a min-max scheme which allows us to prove the existence of critical points...

26. Quantitative topology in Hoelder- and fractional Sobolev-spaces

Armin Schikorra

05/06/2026 10:00

For maps between -spheres we can estimate their degree in terms of their Hoelder- and fractional Sobolev-spaces norm in a sharp way. We will discuss some approaches about a similar estimate for maps from $\mathbb S^3$ to $\mathbb S^2$ and the Hopf degree.
Based on joint works with A. Grzela, K. Mazowiecka, J. Van Schaftingen

27. A high-splay limit of the Oseen-Frank model with electrostatics

Dmitry Golovaty

05/06/2026 11:15

I will present a recent result demonstrating that the Oseen-Frank model which explicitly incorporates electrostatics converges to its highly anisotropic counterpart in which the splay contribution dominates. This is a joint work with Peter Sternberg.

28. Minimality of the vortex solution for Ginzburg-Landau systems

Radu Ignat

05/06/2026 12:00

We consider the standard Ginzburg-Landau system for N-dimensional maps defined in the unit ball for some parameter $\epsilon>0$. For a boundary data corresponding to a vortex of topological degree one, the aim is to prove the (radial) symmetry of the ground state of the system. We show this conjecture in any dimension N≥7 and for every $\epsilon>0$, and then, we also prove it in dimension...

16. Existence of critical points of the n-Ginzburg-Landau energy with prescribed degree 1

Rémy Rodiac

We will discuss the existence of critical points of the $n$-Ginzburg-Landau energy in the unit ball of $\mathbb R^n$ with prescribed degree one on the boundary. We will first prove that there does not exist any minimizer of this energy among maps with prescribed degree $d\neq 0$. Then we will show that we can devise a min-max scheme which allows us to prove the existence of critical points...

25. TBA

Jean Van Schaftingen