{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:3CSK3YIGQWQGM6QY5YU747TXDA","short_pith_number":"pith:3CSK3YIG","schema_version":"1.0","canonical_sha256":"d8a4ade10685a0667a18ee29fe7e7718300cd649ceeafc971aea6afb5d7b54cf","source":{"kind":"arxiv","id":"1111.6776","version":3},"attestation_state":"computed","paper":{"title":"Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Juliette Leblond, Laurent Baratchart, Yannick Fischer","submitted_at":"2011-11-29T11:53:40Z","abstract_excerpt":"We study Hardy spaces $H^p_\\nu$ of the conjugate Beltrami equation $\\bar{\\partial} f=\\nu\\bar{\\partial f}$ over Dini-smooth finitely connected domains, for real contractive $\\nu\\in W^{1,r}$ with $r>2$, in the range $r/(r-1)<p<\\infty$. We develop a theory of conjugate functions and apply it to solve Dirichlet and Neumann problems for the conductivity equation $\\nabla.(\\sigma \\nabla u)=0$ where $\\sigma=(1-\\nu)/(1+\\nu)$. In particular situations, we also consider some density properties of traces of solutions together with boundary approximation issues."},"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":"1111.6776","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-11-29T11:53:40Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d8f142e122f2d552150f59f26ade2537a03330dc11709d525dab050834a644b7","abstract_canon_sha256":"a61b357f7da445bb80d03e7ae4954cfb57833e95a3c50630358d2882196ade0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:35.233102Z","signature_b64":"yy98eaMmY5ZirB+hu2BcbpAkeL3Rjc8a5LkeubpenyC+J8ZSg8t39v3bRHG+tvLG3PpxmmusheAaXYeNbpg7CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8a4ade10685a0667a18ee29fe7e7718300cd649ceeafc971aea6afb5d7b54cf","last_reissued_at":"2026-05-18T04:06:35.232590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:35.232590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Juliette Leblond, Laurent Baratchart, Yannick Fischer","submitted_at":"2011-11-29T11:53:40Z","abstract_excerpt":"We study Hardy spaces $H^p_\\nu$ of the conjugate Beltrami equation $\\bar{\\partial} f=\\nu\\bar{\\partial f}$ over Dini-smooth finitely connected domains, for real contractive $\\nu\\in W^{1,r}$ with $r>2$, in the range $r/(r-1)<p<\\infty$. We develop a theory of conjugate functions and apply it to solve Dirichlet and Neumann problems for the conductivity equation $\\nabla.(\\sigma \\nabla u)=0$ where $\\sigma=(1-\\nu)/(1+\\nu)$. In particular situations, we also consider some density properties of traces of solutions together with boundary approximation issues."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6776","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":"1111.6776","created_at":"2026-05-18T04:06:35.232663+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.6776v3","created_at":"2026-05-18T04:06:35.232663+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6776","created_at":"2026-05-18T04:06:35.232663+00:00"},{"alias_kind":"pith_short_12","alias_value":"3CSK3YIGQWQG","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"3CSK3YIGQWQGM6QY","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"3CSK3YIG","created_at":"2026-05-18T12:26:18.847500+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/3CSK3YIGQWQGM6QY5YU747TXDA","json":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA.json","graph_json":"https://pith.science/api/pith-number/3CSK3YIGQWQGM6QY5YU747TXDA/graph.json","events_json":"https://pith.science/api/pith-number/3CSK3YIGQWQGM6QY5YU747TXDA/events.json","paper":"https://pith.science/paper/3CSK3YIG"},"agent_actions":{"view_html":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA","download_json":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA.json","view_paper":"https://pith.science/paper/3CSK3YIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.6776&json=true","fetch_graph":"https://pith.science/api/pith-number/3CSK3YIGQWQGM6QY5YU747TXDA/graph.json","fetch_events":"https://pith.science/api/pith-number/3CSK3YIGQWQGM6QY5YU747TXDA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA/action/storage_attestation","attest_author":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA/action/author_attestation","sign_citation":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA/action/citation_signature","submit_replication":"https://pith.science/pith/3CSK3YIGQWQGM6QY5YU747TXDA/action/replication_record"}},"created_at":"2026-05-18T04:06:35.232663+00:00","updated_at":"2026-05-18T04:06:35.232663+00:00"}