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Struwe to investigate the Moser-Trudinger functional $E(v)=\\int_{\\Omega} (e^{v^2}-1)dx, v\\in H^1_0(\\Omega).$ We prove that if $u$ blows-up as $t\\to\\infty$ and if $E(u(t,\\cdot))$ remains bounded, then for a sequence $t_k\\to\\infty$ we have $u(t_k,\\cdot)\\rightharpoonup 0$ in $H^1_0$ and $\\|u(t_k,\\cdot)\\|_{H^1_0}^2\\to 4\\pi L$ for an integer $L\\ge 1$.\n  We couple these results with a topologic","authors_text":"Andrea Malchiodi, Francesca De Marchis, Luca Martinazzi","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-29T14:38:53Z","title":"Critical points of the Moser-Trudinger functional"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5576","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0bd5a53d12a95a46c5fe253194e88258416f96e9da877bacaea1199e6ccc2c1d","target":"record","created_at":"2026-05-18T04:12:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"438573b2bbfb251c0624e796154d98a0851274e773fc8161456a59a5f2651a8a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-08-29T14:38:53Z","title_canon_sha256":"69ba2aec70502fffd72cc180c8a4947994d2be5d607058611d62f50e64fc6daa"},"schema_version":"1.0","source":{"id":"1108.5576","kind":"arxiv","version":2}},"canonical_sha256":"9633bbd2f5efe23b34f2414e4106958dfa180dc0924118a4290ec837852b12b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9633bbd2f5efe23b34f2414e4106958dfa180dc0924118a4290ec837852b12b8","first_computed_at":"2026-05-18T04:12:54.294904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:54.294904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y9ovLpwK6kNc8t7IkmiU/nHNLiOosToV/zJ/0kOAHGIHzmWXLIhrFeZ3QsocEgXW7FtemoCQLJonWEbWOTIIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:54.295509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5576","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bd5a53d12a95a46c5fe253194e88258416f96e9da877bacaea1199e6ccc2c1d","sha256:b0fa2d54f14999562750519d6566228d6dbc3faa6885d353ac5de52e91325488"],"state_sha256":"f3057068563921c8fb10dd75131545e1a2f7b4394c1e8ec77acb8d36e66ecc17"}