Carbou, Gilles Regularity for critical points of a non local energy. (English) Zbl 0889.58022 Calc. Var. Partial Differ. Equ. 5, No. 5, 409-433 (1997). The author considers the regularity of critical points of an energy functional defined on \({\mathbf H}^1 (B^3,S^2)\) by \[ E(u)= {1\over 2} \int_{B^3} |\nabla u |^2 -{1\over 2} \int_{B^3} H\cdot u+ \int_{B^3} F(u) \] where \(H\in {\mathbf L}_2 (\mathbb{R}^3, \mathbb{R}^3)\) is a solution of a certain nonlocal problem and \(F\in {\mathcal C}^1 (\mathbb{R}^3, \mathbb{R})\) is a nonlinear term satisfying several growth restrictions. Problems of this sort arise in micromagnetism theory. The author proves that the critical points of \(E\) are smooth except in a subset of one-dimensional Hausdorff measure zero. Reviewer: V.Moroz (Minsk) Cited in 17 Documents MSC: 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 58E20 Harmonic maps, etc. 35B65 Smoothness and regularity of solutions to PDEs 35J20 Variational methods for second-order elliptic equations 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:harmonic maps; regularity; critical points; micromagnetism theory PDFBibTeX XMLCite \textit{G. Carbou}, Calc. Var. Partial Differ. Equ. 5, No. 5, 409--433 (1997; Zbl 0889.58022) Full Text: DOI HAL