REGULARITY FOR CRITICAL POINTS OF A NON LOCAL ENERGY

Gilles Carbou (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

we study the regularity of critical points of an energy which stems from micromagnetism theory. First we show that in dimension two critical points are smooth in B 2. In the three dimensional case we prove that the stationary critical points of the energy are smooth except in a subset of one dimensional Hausdorff measure zero. The particularity of this work is the non local character of one term of the energy.

Domains: Analysis of PDEs [math.AP]

Gilles Carbou. REGULARITY FOR CRITICAL POINTS OF A NON LOCAL ENERGY. Calculus of Variations and Partial Differential Equations, 1997. ⟨hal-01728866⟩