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The Helmholtz decomposition of a BMO type vector field in general unbounded domains

Giga, Yoshikazu Zhongyang, Gu 北海道大学

2023.07.26

概要

Let Ω ⊂ Rn be an open subset. Throughout this entire paper, regarding dimension n we always
consider the case where n ≥ 2 unless otherwise specified. The Helmholtz decomposition of a
vector field f = (f1 , f2 , ..., fn ) defined in Ω is formally of the form
f = f0 + ∇p,
where f0 is a divergence free vector field satisfying supplemental conditions like boundary condition and ∇p denotes the gradient of some scalar function p. For 1 < r < ∞, the Helmholtz
decomposition of Lr (Ω)n is well studied. ...

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