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The aim of the work described in this paper is to determine, via an asymptotic analysis, the limiting form of the free energy governing in the first case 3D ferromagnetic nanowires of infinite length in the limit and in the second case 3D thin films which become infinite when their thickness is vanished. A 1D limit problem on the nanowires and a 2D limit problem on the thin films are obtained. [ABSTRACT FROM AUTHOR]

In this paper, starting from the classical 3D micromagnetic energy, we determine, via an asymptotic analysis, the free energy of two joined ferromagnetic thin films. We distinguish different regimes depending on the limit of the ratio between the small thicknesses of the two films. [ABSTRACT FROM AUTHOR]

The authors consider the problem: −div( p∇ u) = u q−1 + λu, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ n , n ≥ 3, $$ p:\ifmmode\expandafter\bar\else\expandafter\=\fi{\Omega } \to \mathbb{R} $$ is a given positive weight such that $$ p \in H^{1} {\left( \Omega \right)} \cap C{\left( {\ifmmode\expandafter\bar\else\expandafter\=\fi{\Omega }} \right)},\lambda $$ is a real constant and $$ q = \frac{{2n}} {{n - 2}} $$ , and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem. [ABSTRACT FROM AUTHOR]