Transition layers for a spatially inhomogeneous Allen-Cahn equation in multi-dimensional domains (Q765102)

In this paper the authors study a spatially inhomogeneous Allen-Cahn equation in \(N\)-dimensional domains. They obtain a sufficient condition for a hypersurface \(S\) in the domain \(\Omega\) to support stable transition layers, and a necessary condition for \(S\) in \(\Omega\) to support transition layers, not necessarily stable. They also find sharp estimates on depths of transition layers.