A dual approach to regularity in thin film micromagnetics

Melcher, Christof
May 2007
Calculus of Variations & Partial Differential Equations;May2007, Vol. 29 Issue 1, p85
Academic Journal
We prove a regularity result in the two-dimensional theory of soft ferromagnetic films. The associated Euler�Lagrange equation is given by a nonlocal degenerate variational inequality involving fractional derivatives. A difference quotient type argument based on a dual formulation in terms of magnetostatic potentials yields a H�lder estimate for the uniquely determined gradient projection of the magnetization field.


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