{"paper":{"title":"Rotationally symmetric solutions to the Cahn-Hilliard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"\\'Alvaro H\\'ernandez, Michal Kowalczyk","submitted_at":"2015-05-15T17:03:39Z","abstract_excerpt":"This paper is devoted to construction of new solutions to the Cahn-Hilliard equation in $\\mathbb R^d$. Staring from a Delaunay unduloid $D_\\tau$ with parameter $\\tau\\in (0,\\tau^*)$ we find for each sufficiently small $\\varepsilon$ a solution $u$ of this equation which is periodic in the direction of the $x_d$ axis and rotationally symmetric with respect to rotations about this axis. The zero level set of $u$ approaches as $\\varepsilon\\to 0$ the surface $D_\\tau$. We use a refined version of the Lyapunov-Schmidt reduction method which simplifies very technical aspects of previous constructions f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04126","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}