Reflected rough differential equations

In this paper, we study reflected differential equations driven by continuous paths with finite pp-variation (1≤p<21≤p<2) and pp-rough paths (2≤p<32≤p<3) on domains in Euclidean spaces whose boundaries may not be smooth. We define reflected rough differential equations and prove the existence of a solution. Also we discuss the relation between the solution to reflected stochastic differential equation and reflected rough differential equation when the driving process is a Brownian motion.