{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EEKPJ7XTYFPJRZXUBTKV5YYW4E","short_pith_number":"pith:EEKPJ7XT","schema_version":"1.0","canonical_sha256":"2114f4fef3c15e98e6f40cd55ee316e11bd2cffdc253c7d57b00f860d7797866","source":{"kind":"arxiv","id":"1502.06234","version":2},"attestation_state":"computed","paper":{"title":"A semilinear elliptic equation with a mild singularity at $u=0$: existence and homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Giachetti, Fran\\c{c}ois Murat, Pedro J. Mart\\'inez-Aparicio","submitted_at":"2015-02-22T14:53:13Z","abstract_excerpt":"In this paper we consider semilinear elliptic equations with singularities, whose prototype is the following \\begin{equation*} \\begin{cases} \\displaystyle - div \\,A(x) D u = f(x)g(u)+l(x)& \\mbox{in} \\; \\Omega,\\\\ u = 0 & \\mbox{on} \\; \\partial \\Omega,\\\\ \\end{cases} \\end{equation*} where $\\Omega$ is an open bounded set of $\\mathbb{R}^N,\\, N\\geq 1$, $A\\in L^\\infty(\\Omega)^{N\\times N}$ is a coercive matrix, $g:[0,+\\infty)\\rightarrow [0,+\\infty]$ is continuous, and $0\\leq g(s)\\leq {{1}\\over{s^\\gamma}}+1$ $\\forall s>0$, with $0<\\gamma\\leq 1$ and $f,l \\in L^r(\\Omega)$, $r={{2N}\\over{N+2}}$ if $N\\geq 3"},"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":"1502.06234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-22T14:53:13Z","cross_cats_sorted":[],"title_canon_sha256":"26572e196dd1061f055d89b454b19c73d397eaceb96217e98713e3aa14f53464","abstract_canon_sha256":"cd40c029852faaa07befdf81507834f119317fa30cfdf00fb0cfe45a50fcd165"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:21.323007Z","signature_b64":"pobfMMiKq1mypQ2S/uyDPnG8TelMfGcwvvRuMLGE+HCMRIyBvf1sLlOtFF8hvehv7V4Ir3Fc3ufza250IHSbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2114f4fef3c15e98e6f40cd55ee316e11bd2cffdc253c7d57b00f860d7797866","last_reissued_at":"2026-05-18T00:46:21.322629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:21.322629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A semilinear elliptic equation with a mild singularity at $u=0$: existence and homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniela Giachetti, Fran\\c{c}ois Murat, Pedro J. Mart\\'inez-Aparicio","submitted_at":"2015-02-22T14:53:13Z","abstract_excerpt":"In this paper we consider semilinear elliptic equations with singularities, whose prototype is the following \\begin{equation*} \\begin{cases} \\displaystyle - div \\,A(x) D u = f(x)g(u)+l(x)& \\mbox{in} \\; \\Omega,\\\\ u = 0 & \\mbox{on} \\; \\partial \\Omega,\\\\ \\end{cases} \\end{equation*} where $\\Omega$ is an open bounded set of $\\mathbb{R}^N,\\, N\\geq 1$, $A\\in L^\\infty(\\Omega)^{N\\times N}$ is a coercive matrix, $g:[0,+\\infty)\\rightarrow [0,+\\infty]$ is continuous, and $0\\leq g(s)\\leq {{1}\\over{s^\\gamma}}+1$ $\\forall s>0$, with $0<\\gamma\\leq 1$ and $f,l \\in L^r(\\Omega)$, $r={{2N}\\over{N+2}}$ if $N\\geq 3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06234","kind":"arxiv","version":2},"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":"1502.06234","created_at":"2026-05-18T00:46:21.322685+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06234v2","created_at":"2026-05-18T00:46:21.322685+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06234","created_at":"2026-05-18T00:46:21.322685+00:00"},{"alias_kind":"pith_short_12","alias_value":"EEKPJ7XTYFPJ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EEKPJ7XTYFPJRZXU","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EEKPJ7XT","created_at":"2026-05-18T12:29:19.899920+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/EEKPJ7XTYFPJRZXUBTKV5YYW4E","json":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E.json","graph_json":"https://pith.science/api/pith-number/EEKPJ7XTYFPJRZXUBTKV5YYW4E/graph.json","events_json":"https://pith.science/api/pith-number/EEKPJ7XTYFPJRZXUBTKV5YYW4E/events.json","paper":"https://pith.science/paper/EEKPJ7XT"},"agent_actions":{"view_html":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E","download_json":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E.json","view_paper":"https://pith.science/paper/EEKPJ7XT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06234&json=true","fetch_graph":"https://pith.science/api/pith-number/EEKPJ7XTYFPJRZXUBTKV5YYW4E/graph.json","fetch_events":"https://pith.science/api/pith-number/EEKPJ7XTYFPJRZXUBTKV5YYW4E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E/action/storage_attestation","attest_author":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E/action/author_attestation","sign_citation":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E/action/citation_signature","submit_replication":"https://pith.science/pith/EEKPJ7XTYFPJRZXUBTKV5YYW4E/action/replication_record"}},"created_at":"2026-05-18T00:46:21.322685+00:00","updated_at":"2026-05-18T00:46:21.322685+00:00"}