## Regularity for micromagnetic configurations having zero jump energy.(English)Zbl 1021.35023

The authors consider the following family of energy-functionals, related to micromagnetics, that is $E_\varepsilon(u)=\int_\Omega \frac{\varepsilon}{2}|\nabla u|^2+\frac 1{2\varepsilon} \int_{\mathbb{R}^2}H^2_u dx,$ where $$\Omega$$ is a bounded domain of $$\mathbb{R}^2$$, $$u\in H^1(\Omega,S^1)$$ is the vector field corresponding to magnetization and $$H_u$$ is the demagnetizing vector field, defined by $\begin{cases} \text{div}(\overline{u}+Hu)=0 & \text{in }\mathbb{R}^2,\\ \text{curl} H_u=0 & \text{in }\mathbb{R}^2,\end{cases}$ where $$\overline u$$ is the extension of $$u$$ by 0 out of $$\Omega$$. The authors study asymptotic behaviour of $$E_\varepsilon$$.

### MSC:

 35B65 Smoothness and regularity of solutions to PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 35B40 Asymptotic behavior of solutions to PDEs

### Keywords:

magnetization; demagnetizing vector field
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