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Figueroa","submitted_at":"2019-09-03T00:54:05Z","abstract_excerpt":"We consider a sinh-Poisson type equation with variable intensities and Dirichlet boundary condition on a pierced domain \\begin{equation*} \\left\\{ \\begin{array}{ll} \\Delta u +\\rho\\left(V_1(x)e^{u}- V_2(x)e^{-\\tau u}\\right)=0 &\\text{in } \\Omega_\\epsilon:=\\Omega\\setminus \\displaystyle \\bigcup_{i=1}^m \\overline{B(\\xi_i,\\epsilon_i)}\\\\ u=0&\\text{on }\\partial\\Omega_\\epsilon, \\end{array}\\right. \\end{equation*} where $\\rho>0$, $V_1,V_2>0$ are smooth potentials in $\\Omega$, $\\tau>0$, $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^2$ and $B(\\xi_i,\\epsilon_i)$ is a ball centered at $\\xi_i\\in \\Omega$ w"},"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":"1909.00905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-09-03T00:54:05Z","cross_cats_sorted":[],"title_canon_sha256":"375bdf6999a6dcd956f2472d61c3c77856d3bf16d08bda473c91dd8ad1ba3a5e","abstract_canon_sha256":"4186f8e7facca38e8b22633b0cb5eecd624545c79c5d7be47c824a88134cb74a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:37.908957Z","signature_b64":"iQ4NQir13pZQOExgGhsRmvfM+YEr5M01C6xyj0ZXQmUZHTj+CEpiNXixou+YR/0XHj3nWqKNGWh9EPzcZ3pVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0fdd6f8cd5502d60be793015fde237808913e314656e8bfc0a8c08451f77ffa","last_reissued_at":"2026-07-05T00:49:37.908423Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:37.908423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on a sinh-Poisson type equation with variable intensities on pierced domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"P. Figueroa","submitted_at":"2019-09-03T00:54:05Z","abstract_excerpt":"We consider a sinh-Poisson type equation with variable intensities and Dirichlet boundary condition on a pierced domain \\begin{equation*} \\left\\{ \\begin{array}{ll} \\Delta u +\\rho\\left(V_1(x)e^{u}- V_2(x)e^{-\\tau u}\\right)=0 &\\text{in } \\Omega_\\epsilon:=\\Omega\\setminus \\displaystyle \\bigcup_{i=1}^m \\overline{B(\\xi_i,\\epsilon_i)}\\\\ u=0&\\text{on }\\partial\\Omega_\\epsilon, \\end{array}\\right. \\end{equation*} where $\\rho>0$, $V_1,V_2>0$ are smooth potentials in $\\Omega$, $\\tau>0$, $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^2$ and $B(\\xi_i,\\epsilon_i)$ is a ball centered at $\\xi_i\\in \\Omega$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00905","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00905/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1909.00905","created_at":"2026-07-05T00:49:37.908481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.00905v2","created_at":"2026-07-05T00:49:37.908481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.00905","created_at":"2026-07-05T00:49:37.908481+00:00"},{"alias_kind":"pith_short_12","alias_value":"2D65N6GNKUBN","created_at":"2026-07-05T00:49:37.908481+00:00"},{"alias_kind":"pith_short_16","alias_value":"2D65N6GNKUBNMC7H","created_at":"2026-07-05T00:49:37.908481+00:00"},{"alias_kind":"pith_short_8","alias_value":"2D65N6GN","created_at":"2026-07-05T00:49:37.908481+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/2D65N6GNKUBNMC7HSMAV7XRDPA","json":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA.json","graph_json":"https://pith.science/api/pith-number/2D65N6GNKUBNMC7HSMAV7XRDPA/graph.json","events_json":"https://pith.science/api/pith-number/2D65N6GNKUBNMC7HSMAV7XRDPA/events.json","paper":"https://pith.science/paper/2D65N6GN"},"agent_actions":{"view_html":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA","download_json":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA.json","view_paper":"https://pith.science/paper/2D65N6GN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.00905&json=true","fetch_graph":"https://pith.science/api/pith-number/2D65N6GNKUBNMC7HSMAV7XRDPA/graph.json","fetch_events":"https://pith.science/api/pith-number/2D65N6GNKUBNMC7HSMAV7XRDPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA/action/storage_attestation","attest_author":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA/action/author_attestation","sign_citation":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA/action/citation_signature","submit_replication":"https://pith.science/pith/2D65N6GNKUBNMC7HSMAV7XRDPA/action/replication_record"}},"created_at":"2026-07-05T00:49:37.908481+00:00","updated_at":"2026-07-05T00:49:37.908481+00:00"}