{"paper":{"title":"Weighted Energy-Dissipation principle for gradient flows in metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Segatti, Giuseppe Savar\\'e, Riccarda Rossi, Ulisse Stefanelli","submitted_at":"2018-01-15T20:24:51Z","abstract_excerpt":"This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of trajectories \\[ \\mathcal{I}_\\varepsilon[u] = \\int_0^{\\infty} e^{-t/\\varepsilon}\\left( \\frac12 |u'|^2(t) + \\frac1{\\varepsilon}\\phi(u(t)) \\right) \\dd t, \\] featuring the weighted sum of energetic and dissipative terms. As the parameter $\\varepsilon$ is sent to~$0$, the minimizers $u_\\varepsilon$ of such functionals converge, up to subsequences, to curves of maximal slo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04988","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"}