{"paper":{"title":"Stationary layered solutions for a system of Allen-Cahn type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Alessio","submitted_at":"2012-11-25T10:07:25Z","abstract_excerpt":"We consider a class of semilinear elliptic system of the form $-\\Delta u(x,y)+\\nabla W(u(x,y))=0,\\quad (x,y)\\in\\R^{2}$ where $W:\\R^{2}\\to\\R$ is a double well non negative symmetric potential. We show, via variational methods, that if the set of solutions to the one dimensional system $-\\ddot q(x)+\\nabla W(q(x))=0,\\ x\\in\\R$, which connect the two minima of $W$ as $x\\to\\pm\\infty$ has a discrete structure, then the given system has infinitely many layered solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5751","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"}