{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2TS5EINIPRTBKRZTU7UF2YKUG7","short_pith_number":"pith:2TS5EINI","schema_version":"1.0","canonical_sha256":"d4e5d221a87c66154733a7e85d615437dbd334994e38ac61a3f8cad65840d950","source":{"kind":"arxiv","id":"1508.04961","version":1},"attestation_state":"computed","paper":{"title":"On positive solutions of the $(p,A)$-Laplacian with a potential in Morrey space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georgios Psaradakis, Yehuda Pinchover","submitted_at":"2015-08-20T11:38:38Z","abstract_excerpt":"We study qualitative positivity properties of quasilinear equations of the form \\[\n  Q'_{A,p,V}[v] := -\\mathrm{div}(|\\nabla v|_A^{p-2}A(x)\\nabla v) + V(x)|v|^{p-2}v =0 \\qquad x\\in\\Omega, \\] where $\\Omega$ is a domain in $\\mathbb{R}^n$, $1<p<\\infty$, $A=(a_{ij})\\in L^\\infty_{\\rm loc}(\\Omega;\\mathbb{R}^{n\\times n})$ is a symmetric and locally uniformly positive definite matrix, $V$ is a real potential in a certain local Morrey space (depending on $p$), and \\[\n  |\\xi|_{A}^{2}:=A(x)\\xi\\cdot\\xi=\\sum_{i,j=1}^n a_{ij}(x)\\xi_i\\xi_j \\qquad x\\in\\Omega ,~\\xi=(\\xi_1,\\ldots,\\xi_n)\\in \\mathbb{R}^n. \\] Our a"},"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":"1508.04961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-20T11:38:38Z","cross_cats_sorted":[],"title_canon_sha256":"561ca058d37f631b6e9bfdbbfa4785203321ea45a1223e9bd674dea50710bd39","abstract_canon_sha256":"a8227a3b4691bd25e3676f379b4a0f98cf4de4c5df86e417cdc806746b74f296"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:45.696773Z","signature_b64":"rpQ4lEu0+j3SSCDhKhp+sg386kSKUHT4QEQfXNx+BFoO99f525Qxhre9o4x7DxwCOIGS0Rn7N5LxVabCWB25DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4e5d221a87c66154733a7e85d615437dbd334994e38ac61a3f8cad65840d950","last_reissued_at":"2026-05-18T01:02:45.696395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:45.696395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On positive solutions of the $(p,A)$-Laplacian with a potential in Morrey space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Georgios Psaradakis, Yehuda Pinchover","submitted_at":"2015-08-20T11:38:38Z","abstract_excerpt":"We study qualitative positivity properties of quasilinear equations of the form \\[\n  Q'_{A,p,V}[v] := -\\mathrm{div}(|\\nabla v|_A^{p-2}A(x)\\nabla v) + V(x)|v|^{p-2}v =0 \\qquad x\\in\\Omega, \\] where $\\Omega$ is a domain in $\\mathbb{R}^n$, $1<p<\\infty$, $A=(a_{ij})\\in L^\\infty_{\\rm loc}(\\Omega;\\mathbb{R}^{n\\times n})$ is a symmetric and locally uniformly positive definite matrix, $V$ is a real potential in a certain local Morrey space (depending on $p$), and \\[\n  |\\xi|_{A}^{2}:=A(x)\\xi\\cdot\\xi=\\sum_{i,j=1}^n a_{ij}(x)\\xi_i\\xi_j \\qquad x\\in\\Omega ,~\\xi=(\\xi_1,\\ldots,\\xi_n)\\in \\mathbb{R}^n. \\] Our a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04961","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":"1508.04961","created_at":"2026-05-18T01:02:45.696448+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.04961v1","created_at":"2026-05-18T01:02:45.696448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04961","created_at":"2026-05-18T01:02:45.696448+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TS5EINIPRTB","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TS5EINIPRTBKRZT","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TS5EINI","created_at":"2026-05-18T12:29:02.477457+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/2TS5EINIPRTBKRZTU7UF2YKUG7","json":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7.json","graph_json":"https://pith.science/api/pith-number/2TS5EINIPRTBKRZTU7UF2YKUG7/graph.json","events_json":"https://pith.science/api/pith-number/2TS5EINIPRTBKRZTU7UF2YKUG7/events.json","paper":"https://pith.science/paper/2TS5EINI"},"agent_actions":{"view_html":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7","download_json":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7.json","view_paper":"https://pith.science/paper/2TS5EINI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.04961&json=true","fetch_graph":"https://pith.science/api/pith-number/2TS5EINIPRTBKRZTU7UF2YKUG7/graph.json","fetch_events":"https://pith.science/api/pith-number/2TS5EINIPRTBKRZTU7UF2YKUG7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7/action/storage_attestation","attest_author":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7/action/author_attestation","sign_citation":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7/action/citation_signature","submit_replication":"https://pith.science/pith/2TS5EINIPRTBKRZTU7UF2YKUG7/action/replication_record"}},"created_at":"2026-05-18T01:02:45.696448+00:00","updated_at":"2026-05-18T01:02:45.696448+00:00"}