Bubbling solutions for relativistic Abelian Chern-Simons model on a torus
Journal
Communications in Mathematical Physics
Journal Volume
297
Journal Issue
3
Pages
733-758
Date Issued
2010
Author(s)
Yan, S.
Abstract
We prove the existence of bubbling solutions for the following Chern-Simons-Higgs equation: where Ω is a torus. We show that if N > 4 and p1 ≠ pj, j = 2, . . . , N, then for small ε > 0, the above problem has a solution uε, and as ε → 0, uε blows up at the vertex point p1, and satisfies This is the first result for the existence of a solution which blows up at a vertex point. © 2010 Springer-Verlag.
Type
journal article