The inhomogeneous Allen--Cahn equation and the existence of prescribed-mean-curvature hypersurfaces

Costante Bellettini, Neshan Wickramasekera

We prove that for any given compact Riemannian manifold $N$ of dimension $n+1\ge 3$ and any non-negative Lipschitz function $g$ on $N$, there exists a quasi-embedded, boundaryles…