A nonlocal singular perturbation problem with periodic well potential

Kurzke, Matthias

doi:10.1051/cocv:2005037

Cited by 35 publications

(54 citation statements)

References 13 publications

(6 reference statements)

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“…There are also similarities to the approach of Moser [11] who combined interior and boundary vortices, but without calculating a renormalized energy. A different view of (1.1) was pursued in [7], where the functional was reduced to a nonlocal one on the boundary, and aconvergence theorem for the natural scaling was proved. In [7], we could treat an arbitrary continuous periodic potential with −1 (0) = πZ.…”

Section: Fig 1 a Boundary Vortexmentioning

confidence: 99%

Boundary vortices in thin magnetic films

Kurzke

2006

Calc. Var.

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Section: Fig 1 a Boundary Vortexmentioning

confidence: 99%

Boundary vortices in thin magnetic films

Kurzke

2006

Calc. Var.

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“…The connection of this generalized Cahn-Hilliard energy and the corresponding geometrical sharp interface model with line tension has been analyzed by Alberti, Bouchitté and Seppecher in [1,2]. The Gamma-limit for a related energy is derived by Kurzke [15]. The latter energy functional comes from micromagnetism.…”

Section: Related Workmentioning

confidence: 99%

“…According to (16), it can be regarded as a vector field on R × S 1 . According to (15), m ⊥ points inwards on (R − (−1, 1)) × S 1 . According to (14), it does not have a stationary point.…”

Section: Proof Of Propositionmentioning

confidence: 99%

2-d stability of the Néel wall

2006

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We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls.We prove stability of the 1-d transition layer under 2-d perturbations. This amounts to the investigation of the following singularly perturbed energy functional:The topological structure of this two-dimensional problem allows us to use a duality argument to infer the optimal lower bound. The lower bound relies on an -perturbation of the following logarithmically failing interpolation inequality |∇ 1/2 φ| 2 dx sup |φ| |∇φ| dx.

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“…When the nonlinearity f is given by f (u) = sin(cu) for some constant c, problem (1.1) in a half-plane is called the Peierls-Nabarro problem, and it appears as a model of dislocations in crystals (see [21,36]). The Peierls-Nabarro problem is also central to the analysis of boundary vortices in the paper [28], which studies a model for soft thin films in micromagnetism recently derived by Kohn and Slastikov [26] (see also [27]). …”

Section: Introductionmentioning

confidence: 99%