{"paper":{"title":"Lack of compactness in the 2D critical Sobolev embedding, the general case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Hajer Bahouri, Mohamed Majdoub, Nader Masmoudi","submitted_at":"2011-12-13T18:50:51Z","abstract_excerpt":"This paper is devoted to the description of the lack of compactness of the Sobolev embedding of $H^1(\\R^2)$ in the critical Orlicz space ${\\cL}(\\R^2)$. It turns out that up to cores our result is expressed in terms of the concentration-type examples derived by J. Moser in \\cite{M} as in the radial setting investigated in \\cite{BMM}. However, the analysis we used in this work is strikingly different from the one conducted in the radial case which is based on an $L^ \\infty$ estimate far away from the origin and which is no longer valid in the general framework. Within the general framework of $H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2998","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"}