  Although standard planar double bubbles are stable in the sense that the
second variation of the perimeter functional is non-negative for all
area-preserving perturbations the question arises whether they are dynamically
stable. By presenting connections between these two concepts of stability for
double bubbles, we prove that standard planar double bubbles are stable under
the surface diffusion flow via the generalized principle of linearized
stability in parabolic H\"older spaces.
