On the rough Gronwall lemma and its applications

Abstract

We present a rough path analog of the classical Gronwall Lemma introduced recently by A. Deya, M. Gubinelli, M. Hofmanov\'a, S. Tindel in [arXiv:1604.00437] and discuss two of its applications. First, it is applied in the framework of rough path driven PDEs in order to establish energy estimates for weak solutions. Second, it is used in order to prove uniqueness for reflected rough differential equations.