“…Proof of Lemma 3.8. This is a straight-forward adaptation of [34,Lemma 3.13]. Notice first that, from (3.6), (3.5), and Theorem 3.4 it follows that |∂ s θ j i,n | p−2 ∂ s θ j i,n H 1 (I j ) ≤ C(1 + 3 r=1 V r i,n L 2 (I j ) ) (A11) for j = 1, 2, 3 and for all i = 1, .…”