“…Next, we show H ∈ L p (Ω, R 3 ). We prove this by a duality method, which has been used in the proof of [26,Lemma 3.1]. Given F ∈ C ∞ c (Ω, R 3 ) and 1 < r < ∞, by Helmholtz-Weyl decomposition (see [2,Theorem 6.1] or [17,Theorem 2.1]), there exist w ∈ W 1,r (Ω, R 3 ) with ν × w = 0 on ∂Ω, χ ∈ W 1,r (Ω), and z ∈ H N (Ω) such that…”