{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:R6EHGKRLJGU6NTCYTAV35YI7QT","short_pith_number":"pith:R6EHGKRL","schema_version":"1.0","canonical_sha256":"8f88732a2b49a9e6cc58982bbee11f84e2f95d533a7440898a664ec207e1652a","source":{"kind":"arxiv","id":"1507.01730","version":3},"attestation_state":"computed","paper":{"title":"Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hoai-Minh Nguyen","submitted_at":"2015-07-07T09:50:44Z","abstract_excerpt":"In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique introduced in \\cite{Ng-Complementary}, we first derive Cauchy problems from these equations. The limiting absorption principle and the well-posedness are then obtained via various a priori estimates for these Cauchy problems. There approaches are proposed to obtain the a priori estimates. The first one follows from a priori estimates of elliptic systems equ"},"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":"1507.01730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-07T09:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"a0deac2706803d670a1a74c2dd6ddc124837fc55f20a0360f4b62faf47851c88","abstract_canon_sha256":"a9a1d466c230633dc1ff6249e4739a1ca8f467e210ae6d706d223b9c4e4dae36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:02.682002Z","signature_b64":"QlJf8s733uPM9nFrxWzer0LSAhAsyTFBI0P/QuzilskYHsanDd/PHEjKniyvfaujztukd/YtRV7olhMk1dP3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f88732a2b49a9e6cc58982bbee11f84e2f95d533a7440898a664ec207e1652a","last_reissued_at":"2026-05-18T01:26:02.681474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:02.681474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hoai-Minh Nguyen","submitted_at":"2015-07-07T09:50:44Z","abstract_excerpt":"In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique introduced in \\cite{Ng-Complementary}, we first derive Cauchy problems from these equations. The limiting absorption principle and the well-posedness are then obtained via various a priori estimates for these Cauchy problems. There approaches are proposed to obtain the a priori estimates. The first one follows from a priori estimates of elliptic systems equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01730","kind":"arxiv","version":3},"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":"1507.01730","created_at":"2026-05-18T01:26:02.681548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.01730v3","created_at":"2026-05-18T01:26:02.681548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01730","created_at":"2026-05-18T01:26:02.681548+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6EHGKRLJGU6","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6EHGKRLJGU6NTCY","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6EHGKRL","created_at":"2026-05-18T12:29:39.896362+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/R6EHGKRLJGU6NTCYTAV35YI7QT","json":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT.json","graph_json":"https://pith.science/api/pith-number/R6EHGKRLJGU6NTCYTAV35YI7QT/graph.json","events_json":"https://pith.science/api/pith-number/R6EHGKRLJGU6NTCYTAV35YI7QT/events.json","paper":"https://pith.science/paper/R6EHGKRL"},"agent_actions":{"view_html":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT","download_json":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT.json","view_paper":"https://pith.science/paper/R6EHGKRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.01730&json=true","fetch_graph":"https://pith.science/api/pith-number/R6EHGKRLJGU6NTCYTAV35YI7QT/graph.json","fetch_events":"https://pith.science/api/pith-number/R6EHGKRLJGU6NTCYTAV35YI7QT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT/action/storage_attestation","attest_author":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT/action/author_attestation","sign_citation":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT/action/citation_signature","submit_replication":"https://pith.science/pith/R6EHGKRLJGU6NTCYTAV35YI7QT/action/replication_record"}},"created_at":"2026-05-18T01:26:02.681548+00:00","updated_at":"2026-05-18T01:26:02.681548+00:00"}