{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:U2TF5EP7VQ2RX6GXAHHKESIZ7K","short_pith_number":"pith:U2TF5EP7","schema_version":"1.0","canonical_sha256":"a6a65e91ffac351bf8d701cea24919fa80aef7f5d4696d94cff9aab2b51c2f95","source":{"kind":"arxiv","id":"1609.04596","version":1},"attestation_state":"computed","paper":{"title":"On unbounded solutions of ergodic problems in r^m for viscous hamilton-jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"FRDP), Guy Barles (LMPT, Joao Meireles","submitted_at":"2016-09-15T12:29:13Z","abstract_excerpt":"In this article we study ergodic problems in the whole space R m for viscous Hamilton-Jacobi Equations in the case of locally Lips-chitz continuous and coercive right-hand sides. We prove in particular the existence of a critical value $\\lambda$ * for which (i) the ergodic problem has solutions for all $\\lambda$ $\\le$ $\\lambda$ * , (ii) bounded from below solutions exist and are associated to $\\lambda$ * , (iii) such solutions are unique (up to an additive constant). We obtain these properties without additional assumptions in the superquadratic case, while, in the subquadratic one, we assume "},"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":"1609.04596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-15T12:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"9ab348811f643740397b20c5a7aa8ce47b1edd3a9dc922f0714a3dcb9a524655","abstract_canon_sha256":"f846566c098834a663599d251acd90f047e76fe021b64aa4448948af1e5c8baf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:36.274047Z","signature_b64":"9261UNG8s0Y0vx+Jw79ecmREwDIv0zjzA6tLuCKE5nhjG4nDRIFc06AXccaXuQWP3puoB6QGx/GFVuxKrsK2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6a65e91ffac351bf8d701cea24919fa80aef7f5d4696d94cff9aab2b51c2f95","last_reissued_at":"2026-05-18T01:04:36.273526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:36.273526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On unbounded solutions of ergodic problems in r^m for viscous hamilton-jacobi equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"FRDP), Guy Barles (LMPT, Joao Meireles","submitted_at":"2016-09-15T12:29:13Z","abstract_excerpt":"In this article we study ergodic problems in the whole space R m for viscous Hamilton-Jacobi Equations in the case of locally Lips-chitz continuous and coercive right-hand sides. We prove in particular the existence of a critical value $\\lambda$ * for which (i) the ergodic problem has solutions for all $\\lambda$ $\\le$ $\\lambda$ * , (ii) bounded from below solutions exist and are associated to $\\lambda$ * , (iii) such solutions are unique (up to an additive constant). We obtain these properties without additional assumptions in the superquadratic case, while, in the subquadratic one, we assume "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04596","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":"1609.04596","created_at":"2026-05-18T01:04:36.273603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04596v1","created_at":"2026-05-18T01:04:36.273603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04596","created_at":"2026-05-18T01:04:36.273603+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2TF5EP7VQ2R","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2TF5EP7VQ2RX6GX","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2TF5EP7","created_at":"2026-05-18T12:30:46.583412+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/U2TF5EP7VQ2RX6GXAHHKESIZ7K","json":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K.json","graph_json":"https://pith.science/api/pith-number/U2TF5EP7VQ2RX6GXAHHKESIZ7K/graph.json","events_json":"https://pith.science/api/pith-number/U2TF5EP7VQ2RX6GXAHHKESIZ7K/events.json","paper":"https://pith.science/paper/U2TF5EP7"},"agent_actions":{"view_html":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K","download_json":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K.json","view_paper":"https://pith.science/paper/U2TF5EP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04596&json=true","fetch_graph":"https://pith.science/api/pith-number/U2TF5EP7VQ2RX6GXAHHKESIZ7K/graph.json","fetch_events":"https://pith.science/api/pith-number/U2TF5EP7VQ2RX6GXAHHKESIZ7K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K/action/storage_attestation","attest_author":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K/action/author_attestation","sign_citation":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K/action/citation_signature","submit_replication":"https://pith.science/pith/U2TF5EP7VQ2RX6GXAHHKESIZ7K/action/replication_record"}},"created_at":"2026-05-18T01:04:36.273603+00:00","updated_at":"2026-05-18T01:04:36.273603+00:00"}