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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
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