{"paper":{"title":"Metric methods for heteroclinic connections in infinite dimensional spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.AP","authors_text":"Antonin Monteil, Filippo Santambrogio (LM-Orsay)","submitted_at":"2017-09-07T07:38:19Z","abstract_excerpt":"We consider the minimal action problem min \\int\\_R 1/2 |$\\gamma$'|^2 + W($\\gamma$) dt among curves lying in a non-locally-compact metric space and connecting two given zeros of W $\\ge$ 0. For this problem, the optimal curves are usually called heteroclinic connections. We reduce it, following a standard method, to a geodesic problem of the form min \\int\\_0^1 K($\\gamma$)|$\\gamma$'| dt with K = (2W)^(1/2). We then prove existence of curves minimizing this new action under some suitable compactness assumptions on K, which are minimal. The method allows to solve some PDE problems in unbounded doma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02117","kind":"arxiv","version":1},"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"}