Speaker
Description
In this talk, I will present a result on the asymptotic energy-minimizing shape of an isolated magnetized domain ( in both two- and three-dimensional settings. The energy consists of two terms: the first penalizes the interfacial area of the domain, while the second represents the energy of the corresponding magnetostatic field. Here, the magnetostatic potential $h_{\Omega}$ is determined by $\Delta h_{\Omega} = \partial_1 \chi_{\Omega}$, corresponding to uniform magnetization within the domain. In the macroscopic regime $|Ω| \rightarrow\infty$, we derive compactness and $\Gamma$-limit which is formulated in terms of the cross-sectional area of the anisotropically rescaled configuration. I will then explain how to find the solutions for the limit problems. This talk is based on a joint work with Hans Knüpfer.
