Domain dependent monotonicity formula for a singular perturbation problem
Yoshihiro Tonegawa · Indiana University Mathematics Journal · 2003
We consider a singular perturbation problem arising in the scalar phase field model with Keumann boundary conditions on convex domains, and establish a monotonicity formula for general critical points. This gives the Hausdorff distance convergence of the phase boundaries as the parameters tend to ,1ero. We apply the result to stable critical points defined on strictly convex domains, showing that the limit interfaces for stable critical points arc necessarily connected.