{"paper":{"title":"Some Remarks on Pohozaev-Type Identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Da Lio","submitted_at":"2018-11-09T13:34:13Z","abstract_excerpt":"The aim of this note is to discuss in more detail the Pohozaev-type identities that have been recently obtained by the author, Paul Laurain and Tristan Rivi\\`ere in the framework of half-harmonic maps defined either on $R$ or on the sphere $S^1$ with values into a closed manifold $N^n\\subset R^m$. Weak half-harmonic maps are critical points of the following nonlocal energy $$\\int_{R}|(-\\Delta)^{1/4}u|^2 dx~~\\mbox{or}~~\\int_{S^1}|(-\\Delta)^{1/4}u|^2\\ d\\theta.$$\n  If $u$ is a sufficiently smooth critical point of the above energy then it satisfies the following equation of stationarity $$\\frac{d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03893","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"}