On the stability of static domain wall profiles in ferromagnetic thin film (Q2319852)

This article is based on [\textit{G. Carbou}, J. Math. Pures Appl. (9) 93, No. 2, 183--203 (2010; Zbl 1191.35052)]. In the quoted paper the 3d situation is analyzed while in the present paper the authors analyze the 2d case. Of course the problem is simpler and the magnetic field expansion is exactly the same as the one used in the quoted paper (since the field remains 3d). Actually we do not see any change or improvement in the present paper (except the reduction of one variable and notational changes): the estimates are almost all the same with same norms, the proofs are longer (all the details are provided) but the explanations of the approach are shorter so this paper is lengthier and more difficult to read than the quoted paper although it is simpler!