{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:L4O5ZBQSG33JFY5GFXH7VW37VB","short_pith_number":"pith:L4O5ZBQS","schema_version":"1.0","canonical_sha256":"5f1ddc861236f692e3a62dcffadb7fa86554004030e143e038711314961ccdf6","source":{"kind":"arxiv","id":"1306.0099","version":1},"attestation_state":"computed","paper":{"title":"Supercritical problems in domains with thin toroidal holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Seunghyeok Kim","submitted_at":"2013-06-01T12:26:17Z","abstract_excerpt":"In this paper we study the Lane-Emden-Fowler equation $$(P)_\\epsilon\\ \\{\\Delta u+|u|^{q-2}u=0 \\ \\hbox{in}\\ \\mathcal D_\\epsilon, u=0 \\ \\hbox{on}\\ \\partial\\mathcal D_\\epsilon.$$ Here $\\mathcal D_\\epsilon = \\mathcal D \\setminus \\{x \\in \\mathcal D \\ : \\ \\mathrm{dist}(x,\\Gamma_\\ell)\\le \\epsilon\\}$, $\\mathcal D$ is a smooth bounded domain in $\\mathbb{R}^N$, $\\Gamma_\\ell$ is an $\\ell-$dimensional closed manifold such that $\\Gamma_\\ell \\subset \\mathcal D$ with $1\\le \\ell \\le N-3$ and $q={2(N-\\ell)\\over N-\\ell-2}$. We prove that, under some symmetry assumptions, the number of sign changing solutions to"},"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":"1306.0099","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-01T12:26:17Z","cross_cats_sorted":[],"title_canon_sha256":"818bd23c05adfd6ebe4f93269873598e54650f9e2fe6c6bf84caf311e68ca3ba","abstract_canon_sha256":"4a45f628307558e36cf5a97cc58e3e26c5d2c3eb39acee2c962c4bf23274eb49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:56.131899Z","signature_b64":"68a91nbvFgY2U7cBvlP8aNBKlqWUpxTHU4M0h8wTm+zM7G4n9kG5n9GTdDptHgJAiIvCpH/d6xtCOuXwMCx6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f1ddc861236f692e3a62dcffadb7fa86554004030e143e038711314961ccdf6","last_reissued_at":"2026-05-18T03:21:56.131348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:56.131348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Supercritical problems in domains with thin toroidal holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Seunghyeok Kim","submitted_at":"2013-06-01T12:26:17Z","abstract_excerpt":"In this paper we study the Lane-Emden-Fowler equation $$(P)_\\epsilon\\ \\{\\Delta u+|u|^{q-2}u=0 \\ \\hbox{in}\\ \\mathcal D_\\epsilon, u=0 \\ \\hbox{on}\\ \\partial\\mathcal D_\\epsilon.$$ Here $\\mathcal D_\\epsilon = \\mathcal D \\setminus \\{x \\in \\mathcal D \\ : \\ \\mathrm{dist}(x,\\Gamma_\\ell)\\le \\epsilon\\}$, $\\mathcal D$ is a smooth bounded domain in $\\mathbb{R}^N$, $\\Gamma_\\ell$ is an $\\ell-$dimensional closed manifold such that $\\Gamma_\\ell \\subset \\mathcal D$ with $1\\le \\ell \\le N-3$ and $q={2(N-\\ell)\\over N-\\ell-2}$. We prove that, under some symmetry assumptions, the number of sign changing solutions to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0099","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":"1306.0099","created_at":"2026-05-18T03:21:56.131433+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.0099v1","created_at":"2026-05-18T03:21:56.131433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0099","created_at":"2026-05-18T03:21:56.131433+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4O5ZBQSG33J","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4O5ZBQSG33JFY5G","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4O5ZBQS","created_at":"2026-05-18T12:27:51.066281+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/L4O5ZBQSG33JFY5GFXH7VW37VB","json":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB.json","graph_json":"https://pith.science/api/pith-number/L4O5ZBQSG33JFY5GFXH7VW37VB/graph.json","events_json":"https://pith.science/api/pith-number/L4O5ZBQSG33JFY5GFXH7VW37VB/events.json","paper":"https://pith.science/paper/L4O5ZBQS"},"agent_actions":{"view_html":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB","download_json":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB.json","view_paper":"https://pith.science/paper/L4O5ZBQS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.0099&json=true","fetch_graph":"https://pith.science/api/pith-number/L4O5ZBQSG33JFY5GFXH7VW37VB/graph.json","fetch_events":"https://pith.science/api/pith-number/L4O5ZBQSG33JFY5GFXH7VW37VB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB/action/storage_attestation","attest_author":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB/action/author_attestation","sign_citation":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB/action/citation_signature","submit_replication":"https://pith.science/pith/L4O5ZBQSG33JFY5GFXH7VW37VB/action/replication_record"}},"created_at":"2026-05-18T03:21:56.131433+00:00","updated_at":"2026-05-18T03:21:56.131433+00:00"}