Abstract

We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field A is differentiable and its exterior derivative corresponding to the magnetic field dA is bounded. In particular, we prove that, for and , the trace of the magnetic Sobolev space is exactly where for with the convention when . We also characterize fractional magnetic Sobolev spaces as interpolation spaces and give extension theorems from a half-space to the entire space.