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Kogoj","submitted_at":"2019-03-20T12:13:07Z","abstract_excerpt":"We consider the linear second order PDO's $$ \\mathscr{L} = \\mathscr{L}_0 - \\partial_t : = \\sum_{i,j =1}^N \\partial_{x_i}(a_{i,j} \\partial_{x_j} ) - \\sum_{j=i}^N b_j \\partial_{x_j} - \\partial _t,$$and assume that $\\mathscr{L}_0$ has nonnegative characteristic form and satisfies the Ole\\v{\\i}nik--Radkevi\\v{c} rank hypoellipticity condition. These hypotheses allow the construction of Perron-Wiener solutions of the Dirichlet problems for $\\mathscr{L}$ and $\\mathscr{L}_0$ on bounded open subsets of $\\mathbb R^{N+1}$ and of $\\mathbb R^{N}$, respectively.\n  Our main result is the following Tikhonov-t"},"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":"1903.08463","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-20T12:13:07Z","cross_cats_sorted":[],"title_canon_sha256":"df8f2c811885a8e04274f49e6c0bb051347901789f11e0588b6fd54ae9da1639","abstract_canon_sha256":"fcf649b1779010bb35e6c7159af888b7ea3f9d888f9edde7259fe0b38216edbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:48.012914Z","signature_b64":"Xtvlq/o6Zx9EFKV5KphWE6Jfl/Qj4HatkTeaDUnsivlLtykxdLIM1DACByf9mfLr5+Xp3BLLnZteJfMpqbzMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d9df18196638612758e6c12bcaa367c66ac5dfe5a331383ebf786c37267dcb2","last_reissued_at":"2026-05-17T23:50:48.012429Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:48.012429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Dirichlet problem in cylindrical domains for evolution Ole\\v{\\i}nik--Radkevi\\v{c} PDE's: a Tikhonov-type theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessia E. Kogoj","submitted_at":"2019-03-20T12:13:07Z","abstract_excerpt":"We consider the linear second order PDO's $$ \\mathscr{L} = \\mathscr{L}_0 - \\partial_t : = \\sum_{i,j =1}^N \\partial_{x_i}(a_{i,j} \\partial_{x_j} ) - \\sum_{j=i}^N b_j \\partial_{x_j} - \\partial _t,$$and assume that $\\mathscr{L}_0$ has nonnegative characteristic form and satisfies the Ole\\v{\\i}nik--Radkevi\\v{c} rank hypoellipticity condition. These hypotheses allow the construction of Perron-Wiener solutions of the Dirichlet problems for $\\mathscr{L}$ and $\\mathscr{L}_0$ on bounded open subsets of $\\mathbb R^{N+1}$ and of $\\mathbb R^{N}$, respectively.\n  Our main result is the following Tikhonov-t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08463","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":"1903.08463","created_at":"2026-05-17T23:50:48.012500+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.08463v1","created_at":"2026-05-17T23:50:48.012500+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08463","created_at":"2026-05-17T23:50:48.012500+00:00"},{"alias_kind":"pith_short_12","alias_value":"JWO7DAMWMODB","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"JWO7DAMWMODBE5MO","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"JWO7DAMW","created_at":"2026-05-18T12:33:21.387695+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/JWO7DAMWMODBE5MONQJLZKRWPR","json":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR.json","graph_json":"https://pith.science/api/pith-number/JWO7DAMWMODBE5MONQJLZKRWPR/graph.json","events_json":"https://pith.science/api/pith-number/JWO7DAMWMODBE5MONQJLZKRWPR/events.json","paper":"https://pith.science/paper/JWO7DAMW"},"agent_actions":{"view_html":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR","download_json":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR.json","view_paper":"https://pith.science/paper/JWO7DAMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.08463&json=true","fetch_graph":"https://pith.science/api/pith-number/JWO7DAMWMODBE5MONQJLZKRWPR/graph.json","fetch_events":"https://pith.science/api/pith-number/JWO7DAMWMODBE5MONQJLZKRWPR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR/action/storage_attestation","attest_author":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR/action/author_attestation","sign_citation":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR/action/citation_signature","submit_replication":"https://pith.science/pith/JWO7DAMWMODBE5MONQJLZKRWPR/action/replication_record"}},"created_at":"2026-05-17T23:50:48.012500+00:00","updated_at":"2026-05-17T23:50:48.012500+00:00"}