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A Half-Space Theorem for the Allen--Cahn Equation in All Dimensions
Abstract
We prove that, in every dimension, a bounded, non-constant entire solution of the Allen--Cahn equation whose zero set is contained in a half-space is a one-dimensional heteroclinic solution.
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BibTeX
@misc{lee2026halfspace,
title = {{A Half-Space Theorem for the Allen--Cahn Equation in All Dimensions}},
author = {Sanghoon Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15014},
eprint = {2610.15014},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15014},
}
RIS
TY - UNPB
TI - A Half-Space Theorem for the Allen--Cahn Equation in All Dimensions
AU - Sanghoon Lee
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.15014
UR - https://arxiv.org/abs/2610.15014
AB - We prove that, in every dimension, a bounded, non-constant entire solution of the Allen--Cahn equation whose zero set is contained in a half-space is a one-dimensional heteroclinic solution.
ER -