Dept. Math, Hokkaido Univ. EPrints Server

Magnetic clusters and fold energies

Preprint Series # 666
Giga, Yoshikazu and Kubo, Motohiko and Tonegawa, Yoshihiro Magnetic clusters and fold energies. (2004);

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We are concerned with variational properties of a fold energy for a unit, dilation-invariant gradient field (called a cluster) in the unit disk. We show that boundedness of a fold energy implies $L^{1}$-compactness of clusters. We also show that a fold energy is $L^{1}$-lower semicontinuous. We characterize absolute minimizers. We also give a sequence of stationary states and discuss its stability. Surprisingly, the stability depends upon $q$, the power of modulus of the jump discontinuities, in the definition of the fold energy.

Item Type:Preprint
ID Code:433