• Corpus ID: 119707345

Energy minimisers of prescribed winding number in an $\mathbb{S}^1$-valued nonlocal Allen-Cahn type model

@article{Ignat2018EnergyMO,
  title={Energy minimisers of prescribed winding number in an \$\mathbb\{S\}^1\$-valued nonlocal Allen-Cahn type model},
  author={Radu Mihai Ignat and Roger Moser},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
We study a variational model for transition layers in thin ferromagnetic films with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. The model represents the magnetisation by a map from $\mathbb{R}$ to $\mathbb{S}^1$. Thus it has a topological invariant in the form of a winding number, and we study minimisers subject to a prescribed winding number. As shown in our previous paper Ignat-Moser (JDE 2017), the nonlocal term gives rise… 

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