Lower bound for the energy of Bloch walls in micromagnetics. (English) Zbl 1251.78003
The paper under review deals with a model for Bloch walls in micromagnetics. In the first part, an analysis of the one-dimensional case associated to the considered model is developed. This corresponds to the blow-up problem around a jump point for one-dimensional transition layers. Next, the authors study the two-dimensional case and prove relative compactness of families of magnetizations of uniformly bounded energy. A lower bound corresponding to the limit energy is also found. The optimal results for the lower bound problem are based on the study of Lipschitz entropies. These lower bounds coincide with the one-dimensional \(\Gamma\)-limit in some particular cases. In the final part, it is argued that entropies are not appropriate in general for proving the expected sharp lower bound. The proofs combine variational techniques with related entropy methods.
Reviewer: Teodora-Liliana Rădulescu (Craiova)
MSC:
| 78A25 | Electromagnetic theory (general) |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 78M30 | Variational methods applied to problems in optics and electromagnetic theory |
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