  In this paper, we study reflected differential equations driven by continuous
paths with finite $p$-variation ($1\le p<2$) and $p$-rough paths ($2\le p<3$)
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.
