REPRESENTATION OF MAGNETIC FIELDS BY JUMP THEOREM FOR HARMONIC FORMS
U. Cegrell, H. Yamaguchi · Mathematical Proceedings of the Royal Irish Academy · 2008
It has previously been shown that a surface current density J on a closed surface ∑ of class C∞ in ℝ³ induces a static magnetic field B J in ℝ³ \ ∑, which has some discontinuity along ∑. In this note, we represent B J by use of jump theorem for harmonic forms in the case where ∑ is of class Cω We then apply this result to prove the existence of a surface current density J, which induces the nonzero magnetic field B J such that B J = 0 inside (or outside) of the domain bounded by ∑ in ℝ³ . This has previously been called the equilibrium magnetic field for ∑.