Corrigendum: Semiclassical Limit of Quantum Dynamics with Rough Potentials and Well‐Posedness of Transport Equations with Measure Initial Data

Abstract

We would like to correct a few minor mistakes in [2], kindly pointed out to us by Vivek Tewary. In Proposition 2.1 the assumption (ii), involving an L 1 bound on the time derivative, has to be replaced by an L q bound with q > 1, namely:(ii) Time Tightness. There exists q > 1 such that, for all 2 C 1 c .R d / and n 1, the map t 7 ! RAccordingly, in Theorem 5.2, assumption (iv) has to be modified as follows:(iv) Time Tightness. There exists q > 1 such that, for P -a.e. w 2 W , for all 2 C 1 c .R d / and n 1, the map t 7 ! R R d d n .t; i n .w// is absolutely continuous in OE0; T and, uniformly in n,This also applies to [1, theorem 2.3(iv)], where the results of [2] were announced.