Free Boundary Problems 2026

Session

Domain Walls and Patterns in Local and Non-local Geometric Variational Problems

MS-14

8 Sept 2026, 14:00

Humboldt Universität zu Berlin

Conveners

Domain Walls and Patterns in Local and Non-local Geometric Variational Problems: MS-14-1

• Cyrill Muratov (University of Pisa)
• Maria Stella Gelli (Università di Pisa Dipartimento di Matematica)

Description

Organisers: Maria Stella Gelli, Cyrill Muratov

143. Existence and Structure of 360 degree walls in Thin Ferromagnetic Films

Hans Knüpfer (University of Heidelberg)

08/09/2026, 14:00

Domain Walls and Patterns in Local and Non-local Geometric Variational Problems

We study the existence and structure of one-dimensional 360 degree walls in thin uniaxial ferromagnetic films. These structures are topological defects which consist of two oppositely charged 180 degree walls interacting by nonlocal stray-field energy. We show existence for nonzero wall angles when the stray-field interaction is sufficiently weak, while at zero angle no minimizer exists. We...

111. Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth

Chiara Leone (University of Naples Federico II)

08/09/2026, 14:30

Domain Walls and Patterns in Local and Non-local Geometric Variational Problems

Optimal local Lipschitz regularity for scalar almost minimizers of Alt-Caffarelli-type functionals
$$ \mathcal{F}({v}; \Omega) = \int_\Omega \varphi(x,\left|\nabla v(x) \right|)+ \lambda \chi_{\{{v}>0\}} (x) \,dx, $$ with growth function $\varphi$ a generalized Orlicz function, is established.
The results presented in this talk have been obtained in collaboration with Giovanni Scilla...

144. Magnetic domains in finite thin films

Mirco Piccinini (Politecnico di Milano)

08/09/2026, 15:00

Domain Walls and Patterns in Local and Non-local Geometric Variational Problems

I will present an asymptotic analysis of the micromagnetic energy of an ultrathin ferromagnetic material of finite spatial extent, subject to strong uniaxial anisotropy with easy axis perpendicular to the film plane. In this regime, a suitable regularization is required to account for possible jump discontinuities of the magnetization at the sample boundary, which would produce infinite...

157. Magnetic skyrmions beyond the conformal limit

Theresa Simon (University of Münster)

08/09/2026, 15:30

Domain Walls and Patterns in Local and Non-local Geometric Variational Problems

In the radial setting, we analyze how magnetic skyrmions transition to (large scale) bubbles in the entire regime of positive energetic cost of domain walls, i.e., far away from the conformal limit. First, we demonstrate existence of radial, skyrmionic bubbles throughout this maximal regime of energetic feasibility. Second, we perform a Gamma-convergence analysis in the limit of vanishing...