A singular perturbation problem for the fractional Allen-Cahn equation
I will describe some convergence result for a singular perturbation of the fractional Allen-Chan equation involving powers of the laplacian less than 1/2. In this case, one converges in a suitable sense to stationary minimal nonlocal surfaces that I will describe precisely. The convergence happens to be strong due to a deep result of Geometric Measure Theory due to Marstrand. This is a feature of the non locality of the problem.