LAUSR

In the proof of theorem 4.1, the sequence Uη, j, which is established in lemma 3.4, only converges in Ωt to the oscillating decaying solution uω,t,χt ,ξ,N . Therefore, we can not use (4.2) when t > t∗, and the assertion in case (b) is incorrect. We have to modify it to be an assertion about t = t∗, which corresponds to the case when Ωt and D are just touched, and in doing so we need the stronger assumption that D has a Lipschitz boundary. With this modification, it turns out that |Iω,t,χt(τ )| in (b) has a lower bound of order τ 2−n, while that in (a) is of exponential decay in τ . The modified statement is given below.