On the Chern–Simons limit for a Maxwell–Chern–Simons model on bounded domains

Abstract

This paper concerns the Chern–Simons limit for the Abelian Maxwell–Chern–Simons model on bounded domains with vanishing gauge fields. We prove that every sequence of solutions of the Maxwell–Chern–Simons equations has a subsequence converging to a solution of the Chern–Simons equation in any C k norms. We also show that the Maxwell–Chern–Simons equations with the nontopological type boundary condition do not admit any nontrivial solutions on star-shaped domains.