English

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

Differential Geometry 2019-03-19 v1 Analysis of PDEs

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 Ritor\'e.

Keywords

Cite

@article{arxiv.1903.03185,
  title  = {On the concentration for a singularly perturbed problem with nonlinear Neumann boundary condition},
  author = {Eduardo Hitomi},
  journal= {arXiv preprint arXiv:1903.03185},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-23T08:01:44.307Z