{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:W3MIB2KL2RH6DWQF5KR3PXET3Z","short_pith_number":"pith:W3MIB2KL","schema_version":"1.0","canonical_sha256":"b6d880e94bd44fe1da05eaa3b7dc93de75b50e2a4dd21d8f6f9ea310fe23a081","source":{"kind":"arxiv","id":"1611.00412","version":2},"attestation_state":"computed","paper":{"title":"A nonlinear free boundary problem with a self-driven Bernoulli condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram Karakhanyan, Enrico Valdinoci, Serena Dipierro","submitted_at":"2016-11-01T22:41:17Z","abstract_excerpt":"We study a Bernoulli type free boundary problem with two phases $$J[u]=\\int_{\\Omega}|\\nabla u(x)|^2\\,dx+\\Phi\\big({\\mathcal M}_-(u), {\\mathcal{M}}_+(u)\\big), \\quad u-\\bar u\\in W^{1,2}_0(\\Omega), $$ where $\\bar u\\in W^{1,2}(\\Omega)$ is a given boundary datum. Here, ${\\mathcal M}_1$ and ${\\mathcal M}_2$ are weighted volumes of $\\{u\\le 0\\}\\cap \\Omega$ and $\\{u>0\\}\\cap \\Omega$, respectively, and $\\Phi$ is a nonnegative function of two real variables.\n  We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and"},"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":"1611.00412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-11-01T22:41:17Z","cross_cats_sorted":[],"title_canon_sha256":"461b17e25fa56eda83458ece90f563e6f6122ec79e8433695a1dc9c440941e70","abstract_canon_sha256":"ed6fe5bcef295c495899ad778e48e5d54b028adc6e1295201a282eff03214448"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:03.778240Z","signature_b64":"KMFj1Ku+rmLFGCOQ1QpDNQI33ZfZ/XfGHPSC+cZ1XBVuy7mHRyjqQMpTOaVFyDEDwNxAMeBiReqR6EfCm3j2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6d880e94bd44fe1da05eaa3b7dc93de75b50e2a4dd21d8f6f9ea310fe23a081","last_reissued_at":"2026-05-18T00:52:03.777544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:03.777544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A nonlinear free boundary problem with a self-driven Bernoulli condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram Karakhanyan, Enrico Valdinoci, Serena Dipierro","submitted_at":"2016-11-01T22:41:17Z","abstract_excerpt":"We study a Bernoulli type free boundary problem with two phases $$J[u]=\\int_{\\Omega}|\\nabla u(x)|^2\\,dx+\\Phi\\big({\\mathcal M}_-(u), {\\mathcal{M}}_+(u)\\big), \\quad u-\\bar u\\in W^{1,2}_0(\\Omega), $$ where $\\bar u\\in W^{1,2}(\\Omega)$ is a given boundary datum. Here, ${\\mathcal M}_1$ and ${\\mathcal M}_2$ are weighted volumes of $\\{u\\le 0\\}\\cap \\Omega$ and $\\{u>0\\}\\cap \\Omega$, respectively, and $\\Phi$ is a nonnegative function of two real variables.\n  We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00412","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":"1611.00412","created_at":"2026-05-18T00:52:03.777656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.00412v2","created_at":"2026-05-18T00:52:03.777656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00412","created_at":"2026-05-18T00:52:03.777656+00:00"},{"alias_kind":"pith_short_12","alias_value":"W3MIB2KL2RH6","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"W3MIB2KL2RH6DWQF","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"W3MIB2KL","created_at":"2026-05-18T12:30:48.956258+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/W3MIB2KL2RH6DWQF5KR3PXET3Z","json":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z.json","graph_json":"https://pith.science/api/pith-number/W3MIB2KL2RH6DWQF5KR3PXET3Z/graph.json","events_json":"https://pith.science/api/pith-number/W3MIB2KL2RH6DWQF5KR3PXET3Z/events.json","paper":"https://pith.science/paper/W3MIB2KL"},"agent_actions":{"view_html":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z","download_json":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z.json","view_paper":"https://pith.science/paper/W3MIB2KL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.00412&json=true","fetch_graph":"https://pith.science/api/pith-number/W3MIB2KL2RH6DWQF5KR3PXET3Z/graph.json","fetch_events":"https://pith.science/api/pith-number/W3MIB2KL2RH6DWQF5KR3PXET3Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z/action/storage_attestation","attest_author":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z/action/author_attestation","sign_citation":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z/action/citation_signature","submit_replication":"https://pith.science/pith/W3MIB2KL2RH6DWQF5KR3PXET3Z/action/replication_record"}},"created_at":"2026-05-18T00:52:03.777656+00:00","updated_at":"2026-05-18T00:52:03.777656+00:00"}