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 d≥1 and p>1, the trace of the magnetic Sobolev space WA1,p(R+d+1) is exactly WA∥1−1/p,p(Rd) where A∥(x)=(A1,…,Ad)(x,0) for x∈Rd with the convention A=(A1,…,Ad+1) when A∈C1(R+d+1‾,Rd+1). We also characterize fractional magnetic Sobolev spaces as interpolation spaces and give extension theorems from a half-space to the entire space.
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