Generalized fractional smoothness and $L_p$-variation of BSDEs with non-Lipschitz terminal condition

We relate the $L_p$-variation, $2\le p<\mathrm{\infty }$, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.