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We give a complete description of the asymptotic behavior of $u_p$ as $p\\rightarrow +\\infty$, under the condition \\[p\\int_{\\Omega} |\\nabla u_p|^2\\,dx\\rightarrow \\beta\\in\\mathbb R\\qquad\\mbox{ as $p\\rightarrow +\\infty$}.\\]"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.05659","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-19T17:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"6f84c934ffab7e13c35f35e08834e7efe0b9f4c2eecb7dcc3a2c7109680db956","abstract_canon_sha256":"4e0d042e78bd0f1cdf1c19d547be37e3ed50049411881bce563881649b2a9602"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:46.349634Z","signature_b64":"SX9rCLO2O6dD4gK/qpt5B4xP7KZHlZVglAPPSQwoB9d4LvYffxsrwaVURWviQjWv2qjcDevCg2dmtvCAKWV1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64aea5a2253f0e72a30241f40beeccd7679f0519a7bc0b465897c79a3d5b08c9","last_reissued_at":"2026-05-18T01:10:46.349127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:46.349127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic profile of positive solutions of Lane-Emden problems in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Francesca De Marchis, Isabella Ianni","submitted_at":"2016-07-19T17:01:02Z","abstract_excerpt":"We consider families $u_p$ of solutions to the problem \\begin{equation}\\label{problemAbstract} \\left\\{\\begin{array}{lr}-\\Delta u= u^p & \\mbox{ in }\\Omega\\\\ u>0 & \\mbox{ in }\\Omega\\\\ u=0 & \\mbox{ on }\\partial \\Omega \\end{array}\\right.\\tag{$\\mathcal E_p$} \\end{equation} where $p>1$ and $\\Omega$ is a smooth bounded domain of $\\mathbb R^2$. We give a complete description of the asymptotic behavior of $u_p$ as $p\\rightarrow +\\infty$, under the condition \\[p\\int_{\\Omega} |\\nabla u_p|^2\\,dx\\rightarrow \\beta\\in\\mathbb R\\qquad\\mbox{ as $p\\rightarrow +\\infty$}.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05659","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.05659","created_at":"2026-05-18T01:10:46.349205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05659v1","created_at":"2026-05-18T01:10:46.349205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05659","created_at":"2026-05-18T01:10:46.349205+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSXKLIRFH4HH","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSXKLIRFH4HHFIYC","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSXKLIRF","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25","json":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25.json","graph_json":"https://pith.science/api/pith-number/MSXKLIRFH4HHFIYCIH2AX3WM25/graph.json","events_json":"https://pith.science/api/pith-number/MSXKLIRFH4HHFIYCIH2AX3WM25/events.json","paper":"https://pith.science/paper/MSXKLIRF"},"agent_actions":{"view_html":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25","download_json":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25.json","view_paper":"https://pith.science/paper/MSXKLIRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05659&json=true","fetch_graph":"https://pith.science/api/pith-number/MSXKLIRFH4HHFIYCIH2AX3WM25/graph.json","fetch_events":"https://pith.science/api/pith-number/MSXKLIRFH4HHFIYCIH2AX3WM25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25/action/storage_attestation","attest_author":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25/action/author_attestation","sign_citation":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25/action/citation_signature","submit_replication":"https://pith.science/pith/MSXKLIRFH4HHFIYCIH2AX3WM25/action/replication_record"}},"created_at":"2026-05-18T01:10:46.349205+00:00","updated_at":"2026-05-18T01:10:46.349205+00:00"}