On the optimality of stripes in a variational model with non-local   interactions
  We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $\Gamma$--convergence analysis, we show that as the parameter J converges to a critical value J c, the minimizers converge to periodic one-dimensional stripes. A similar analysis has been previously performed by other authors for related discrete systems. In that context, a central point is that each " angle " comes with a strictly positive contribution to the energy. Since this is not anymore the case in the continuous setting, we need to overcome this difficulty by slicing arguments and a rigidity result. 
Michael Goldman (LJLL), Eris Runa (MPI-MIS)
math.AP math-ph math.MP