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 W A 1 , p ( R + d + 1 ) is exactly W A ∥ 1 − 1 / p , p ( R d ) where A ∥ ( x ) = ( A 1 , … , A d ) ( x , 0 ) for x ∈ R d with the convention A = ( A 1 , … , A d + 1 ) when A ∈ C 1 ( R + d + 1 ‾ , R d + 1 ) . We also characterize fractional magnetic Sobolev spaces as interpolation spaces and give extension theorems from a half-space to the entire space.

中文翻译：

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磁 Sobolev 空间中函数边界上迹的表征

摘要 我们刻画了在半空间或光滑有界域中定义的磁 Sobolev 空间的迹，其中磁场 A 是可微的，其对应于磁场 dA 的外导数是有界的。特别地，我们证明，对于 d ≥ 1 且 p > 1 ，磁 Sobolev 空间的迹线 WA 1 , p ( R + d + 1 ) 恰好是 WA ∥ 1 − 1 / p , p ( R d ) 其中A ∥ ( x ) = ( A 1 , … , A d ) ( x , 0 ) 对于 x ∈ R d 与约定 A = ( A 1 , … , A d + 1 ) 当 A ∈ C 1 ( R + d + 1 ‾ , R d + 1 ) 。我们还将分数磁 Sobolev 空间表征为插值空间，并给出从半空间到整个空间的扩展定理。