{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7NDHTTG4ZFUI3LJSDDAGRT5LUR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"853b750c4987661e6a698056910a641efea65fe207bde89b97b89b8bd2e534f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T22:34:42Z","title_canon_sha256":"ba5f4518eb7959dec285eca2a6a4c5cf34a6a861a1782fd725a15e603255f9cd"},"schema_version":"1.0","source":{"id":"1602.02808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02808","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02808v1","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02808","created_at":"2026-05-18T01:21:08Z"},{"alias_kind":"pith_short_12","alias_value":"7NDHTTG4ZFUI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7NDHTTG4ZFUI3LJS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7NDHTTG4","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:aeef778c279f882738c765b969cdb03ccbdceb5c1c95922a791bf6dcca902b47","target":"graph","created_at":"2026-05-18T01:21:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Aleksandar Mojsic, Michel Chipot, Prosenjit Roy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T22:34:42Z","title":"On some Variational Problems set on domains tending to infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02808","kind":"arxiv","version":1},"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:c90e812027e9c126a1f97ac685942e5e9146a0b4e9e9b49cb5b5f50de4a1d382","target":"record","created_at":"2026-05-18T01:21:08Z","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":"853b750c4987661e6a698056910a641efea65fe207bde89b97b89b8bd2e534f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-08T22:34:42Z","title_canon_sha256":"ba5f4518eb7959dec285eca2a6a4c5cf34a6a861a1782fd725a15e603255f9cd"},"schema_version":"1.0","source":{"id":"1602.02808","kind":"arxiv","version":1}},"canonical_sha256":"fb4679ccdcc9688dad3218c068cfaba45facf4df517970ba4a4fcebe16a9c53f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb4679ccdcc9688dad3218c068cfaba45facf4df517970ba4a4fcebe16a9c53f","first_computed_at":"2026-05-18T01:21:08.082975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:08.082975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DCyklNUYmG6yUWbpWofBe5Je4U2/gXdBO7d4C/jYdlFtBOG+zqysVitsf6WfDqrn4l9qirYPP8odmfDh0lR1AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:08.083626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c90e812027e9c126a1f97ac685942e5e9146a0b4e9e9b49cb5b5f50de4a1d382","sha256:aeef778c279f882738c765b969cdb03ccbdceb5c1c95922a791bf6dcca902b47"],"state_sha256":"0900382899d9f08f204423e5b83184f1ce8bbedcf76cef3b1a7219d6df0c5fed"}