  We investigate the dynamics of roll solutions at the zigzag boundary of the
planar Swift-Hohenberg equation. Linear analysis shows an algebraic decay of
small perturbation with a $t^{- 1/4}$ rate, instead of the classical $t^{-
1/2}$ diffusive decay rate, due to the degeneracy of the quadratic term of the
continuation of the translational mode of the linearized operator in the
Bloch-Fourier spaces. The proof is based on a decomposition of the neutral mode
and the faster decaying modes in the Bloch-Fourier space, and a fixed-point
argument, demonstrating the irrelevancy of the nonlinear terms.
