A compactness result for periodic multivortices in the electroweak theory Original Research Article

We derive a priori uniform bounds for solutions of an elliptic system of Liouville-type equations, first analyzed by J. Spruck and Y. Yang (Comm. Math. Phys. 144 (1992) 1), yielding periodic multivortices in the classical electroweak theory of Glashow–Salam–Weinberg. Our proof is based on a concentration–quantization result, in the same spirit of Brezis–Merle (Comm. Partial Differential Equations 16 (8,9) (1991) 1223) and Li–Shafrir (Indiana Univ. Math. J. 43 (4) (1994) 1255), for mean field equations on Riemannian compact 2-manifolds.