It has been recently shown that strictly stable critical
configurations for the Ohta-Kawasaki energy are in fact isolated local
minimizers with respect to small $L^1$-perturbations. After reviewing such
results and some of their applications, we consider the associated evolution
problem. More precisely, we show that such strictly stable configurations
are exponentially stable for the $H^{-1/2}$-gradient flow of the Ohta-Kawasaki
energy, also known as the nonlocal (or modified) Mullins-Sekerka flow. http://cvgmt.sns.it/seminar/519/
