7 problems

Let $u$ be the stray-field potential on ${\mathbb R}^3$, and let $\boldsymbol M$ be the magnetization in a domain $\Omega$. Assume that $u\in W^2_2({\mathbb R}^3)$; equivalently, a…

Let $\Omega\subset\mathbb R^2$ be a smooth, simply connected, bounded convex domain, and let $m_\varepsilon$ be minimizers of the Aviles–Giga functional … subject to…

Let $h$ denote the applied field, and let magnetisations be configurations governed by the Landau–Lifshitz–Gilbert equation in a nanowire with Dzyaloshinskii–Moriya interaction. A…

Let $\Omega$ be the domain and let $u\in {\mathcal M}_{\rm div}(\Omega)$, with lifting $\phi$ and associated jump set $J$ and measure $\nu$. For functions in…

Micromagnetic line-energy conjecture. Some line energies $\mathcal{I}_f$ arising from micromagnetics are conjectured to be the $\Gamma$-limit of the corresponding functionals in th…

First-order Gamma-convergence conjecture. At first order, $F_\theta$ $\Gamma$-converges to $F^{(0)}$ in the weak $\dot{H}^1$-topology as $\theta\downarrow0$.

Boundary-vortex energy conjecture. The energetic cost of a boundary vortex remains of order