{"paper":{"title":"Minimising movements for oscillating energies: the critical regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Andrea Braides, Johannes Zimmer, Nadia Ansini","submitted_at":"2016-05-06T10:36:17Z","abstract_excerpt":"Minimising movements are investigated for an energy which is the superposition of a convex functional and fast small oscillations. Thus a minimising movement scheme involves a temporal parameter $\\tau$ and a spatial parameter $\\epsilon$, with $\\tau$ describing the time step and the frequency of the oscillations being proportional to $\\frac 1 \\epsilon$. The extreme cases of fast time scales $\\tau << \\epsilon$ and slow time scales $\\epsilon << \\tau$ have been investigated in Braides, Springer Lecture Notes 2094 (2014). In this article, the intermediate (critical) case of finite ratio $\\epsilon/\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01885","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"}