On the internal transition layer to some inhomogeneous semilinear problems: Interface location

Abstract

We are concerned with the location of the internal transition layer for some classes of solutions to an inhomogeneous one-dimensional elliptic problem with Neumann boundary conditions. We generalize and extend some known results with a variational method based on the Young's inequality and the co-area formula. As an application, we establish the location of the internal transition layer to the problem posed on some symmetric Riemannian manifolds.