An Imbedding Theorem for a Hilbert Space Appearing in Electromagnetics
Satoshi Kaizu, Fumio Kikuchi · Institutional Repositories DataBase (IRDB) · 1986
Let Ω be a bounded domain in R$F^3$ with a Lipschitz continuous boundary αΩ. In electromagnetics, we consider a Hilbert space of vector-valued functions which, along with their rotations and divergences, are square summable in Ω and whose normal components on αΩ vanish. We will show that this space is continuously imbedded to {H$F^1$(Ω)}$F^3$ when Ω is convex, where H$F^1$(Ω) is the usual first order Sobolev space. In addition, we will derive an inequality for functions in this Hilbert space. To these aims, we adopt the techniques of Kadlec-Grisvard and the mixed formulation.