### Abstract

In this paper, we develop a new representation for outgoing solutions to the time harmonic Maxwell equations in unbounded domains in R{double struck}^{3}. This representation leads to a Fredholm integral equation of the second kind for solving the problem of scattering from a perfect conductor, which does not suffer from spurious resonances or low-frequency breakdown, although it requires the inversion of the scalar surface Laplacian on the domain boundary. In the course of our analysis, we give a new proof of the existence of nontrivial families of time-harmonic solutions with vanishing normal components that arise when the boundary of the domain is not simply connected. We refer to these as k-Neumann fields, since they generalize, to nonzero wave numbers, the classical harmonic Neumann fields. The existence of k-Neumann fields was established earlier by Kress.

Original language | English (US) |
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Pages (from-to) | 413-463 |

Number of pages | 51 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 63 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1 2010 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics