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.
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