On the concentration for a singularly perturbed problem with nonlinear Neumann boundary condition

Abstract

In this work, we prove the existence of a family of solutions of the Allen-Cahn equation with nonlinear Neumann boundary condition under some constraints, whose nodal sets concentrate asymptotically to a given volume nondegenerate capillary hypersurface in a compact Riemannian manifold. Our construction is inspired by the works of Pacard and of Pacard and Ritoré.

arXiv admin note: text overlap with arXiv:math/0302160 by other authors

References in corpus (2)

• A singular perturbation limit of diffused interface energy with a fixed contact angle condition
• A polyhedron comparison theorem for 3-manifolds with positive scalar curvature