{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7NDHTTG4ZFUI3LJSDDAGRT5LUR","short_pith_number":"pith:7NDHTTG4","schema_version":"1.0","canonical_sha256":"fb4679ccdcc9688dad3218c068cfaba45facf4df517970ba4a4fcebe16a9c53f","source":{"kind":"arxiv","id":"1602.02808","version":1},"attestation_state":"computed","paper":{"title":"On some Variational Problems set on domains tending to infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aleksandar Mojsic, Michel Chipot, Prosenjit Roy","submitted_at":"2016-02-08T22:34:42Z","abstract_excerpt":"Let $\\Omega_\\ell = \\ell\\omega_1 \\times \\omega_2$ where $\\omega_1 \\subset \\R^p$ and $\\omega_2 \\subset \\R^{n-p}$ are assumed to be open and bounded. We consider the following minimization problem: $$E_{\\Omega_\\ell}(u_\\ell) = \\min_{u\\in W_0^{1,q}(\\Omega_\\ell)}E_{\\Omega_\\ell}(u)$$ where $E_{\\Omega_\\ell}(u) = \\int_{\\Omega_\\ell}F(\\grad u)-fu$, $F$ is a convex function and $f\\in L^{q'}(\\omega_2)$. We are interested in studying the asymptotic behavior of the solution $u_\\ell$ as $\\ell$ tends to infinity."},"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":"1602.02808","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T22:34:42Z","cross_cats_sorted":[],"title_canon_sha256":"ba5f4518eb7959dec285eca2a6a4c5cf34a6a861a1782fd725a15e603255f9cd","abstract_canon_sha256":"853b750c4987661e6a698056910a641efea65fe207bde89b97b89b8bd2e534f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:08.083626Z","signature_b64":"DCyklNUYmG6yUWbpWofBe5Je4U2/gXdBO7d4C/jYdlFtBOG+zqysVitsf6WfDqrn4l9qirYPP8odmfDh0lR1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb4679ccdcc9688dad3218c068cfaba45facf4df517970ba4a4fcebe16a9c53f","last_reissued_at":"2026-05-18T01:21:08.082975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:08.082975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some Variational Problems set on domains tending to infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aleksandar Mojsic, Michel Chipot, Prosenjit Roy","submitted_at":"2016-02-08T22:34:42Z","abstract_excerpt":"Let $\\Omega_\\ell = \\ell\\omega_1 \\times \\omega_2$ where $\\omega_1 \\subset \\R^p$ and $\\omega_2 \\subset \\R^{n-p}$ are assumed to be open and bounded. We consider the following minimization problem: $$E_{\\Omega_\\ell}(u_\\ell) = \\min_{u\\in W_0^{1,q}(\\Omega_\\ell)}E_{\\Omega_\\ell}(u)$$ where $E_{\\Omega_\\ell}(u) = \\int_{\\Omega_\\ell}F(\\grad u)-fu$, $F$ is a convex function and $f\\in L^{q'}(\\omega_2)$. We are interested in studying the asymptotic behavior of the solution $u_\\ell$ as $\\ell$ tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02808","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":"1602.02808","created_at":"2026-05-18T01:21:08.083066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.02808v1","created_at":"2026-05-18T01:21:08.083066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02808","created_at":"2026-05-18T01:21:08.083066+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NDHTTG4ZFUI","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NDHTTG4ZFUI3LJS","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NDHTTG4","created_at":"2026-05-18T12:30:04.600751+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/7NDHTTG4ZFUI3LJSDDAGRT5LUR","json":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR.json","graph_json":"https://pith.science/api/pith-number/7NDHTTG4ZFUI3LJSDDAGRT5LUR/graph.json","events_json":"https://pith.science/api/pith-number/7NDHTTG4ZFUI3LJSDDAGRT5LUR/events.json","paper":"https://pith.science/paper/7NDHTTG4"},"agent_actions":{"view_html":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR","download_json":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR.json","view_paper":"https://pith.science/paper/7NDHTTG4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.02808&json=true","fetch_graph":"https://pith.science/api/pith-number/7NDHTTG4ZFUI3LJSDDAGRT5LUR/graph.json","fetch_events":"https://pith.science/api/pith-number/7NDHTTG4ZFUI3LJSDDAGRT5LUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR/action/storage_attestation","attest_author":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR/action/author_attestation","sign_citation":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR/action/citation_signature","submit_replication":"https://pith.science/pith/7NDHTTG4ZFUI3LJSDDAGRT5LUR/action/replication_record"}},"created_at":"2026-05-18T01:21:08.083066+00:00","updated_at":"2026-05-18T01:21:08.083066+00:00"}