{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GRBVGW2I2VMJNIVTSEUZTD5UPG","short_pith_number":"pith:GRBVGW2I","schema_version":"1.0","canonical_sha256":"3443535b48d55896a2b39129998fb4799f96e62f4f010a65a45cfa0e7fcac410","source":{"kind":"arxiv","id":"1301.2962","version":1},"attestation_state":"computed","paper":{"title":"Existence of solution to a critical trace equation with variable exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Analia Silva, Julian Fernandez Bonder, Nicolas Saintier","submitted_at":"2013-01-14T13:04:05Z","abstract_excerpt":"In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the $p(x)-$Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies on a suitable generalization of the concentration--compactness principle for the trace embedding for variable exponent Sobolev spaces and the classical mountain pass theorem."},"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":"1301.2962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-14T13:04:05Z","cross_cats_sorted":[],"title_canon_sha256":"e5cdf1619996fd76ebbee1f4363261b87b9ac8ff546e8ffbb1dd80a015267476","abstract_canon_sha256":"21b57dcc4f646082f7f84485e26c66a8b920f14c0ec8c00e0077318747e69aa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:27.715496Z","signature_b64":"MKsT6a7L9EJ48H73hkiWG4LItVESruP4p53/rMD6hyS+SkSaWQftpMnJ9bO7mCmjhdWArfsrwktIxncT3OSrBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3443535b48d55896a2b39129998fb4799f96e62f4f010a65a45cfa0e7fcac410","last_reissued_at":"2026-05-18T03:36:27.715114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:27.715114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of solution to a critical trace equation with variable exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Analia Silva, Julian Fernandez Bonder, Nicolas Saintier","submitted_at":"2013-01-14T13:04:05Z","abstract_excerpt":"In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the $p(x)-$Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies on a suitable generalization of the concentration--compactness principle for the trace embedding for variable exponent Sobolev spaces and the classical mountain pass theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2962","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":"1301.2962","created_at":"2026-05-18T03:36:27.715166+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.2962v1","created_at":"2026-05-18T03:36:27.715166+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2962","created_at":"2026-05-18T03:36:27.715166+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRBVGW2I2VMJ","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRBVGW2I2VMJNIVT","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRBVGW2I","created_at":"2026-05-18T12:27:45.050594+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/GRBVGW2I2VMJNIVTSEUZTD5UPG","json":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG.json","graph_json":"https://pith.science/api/pith-number/GRBVGW2I2VMJNIVTSEUZTD5UPG/graph.json","events_json":"https://pith.science/api/pith-number/GRBVGW2I2VMJNIVTSEUZTD5UPG/events.json","paper":"https://pith.science/paper/GRBVGW2I"},"agent_actions":{"view_html":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG","download_json":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG.json","view_paper":"https://pith.science/paper/GRBVGW2I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.2962&json=true","fetch_graph":"https://pith.science/api/pith-number/GRBVGW2I2VMJNIVTSEUZTD5UPG/graph.json","fetch_events":"https://pith.science/api/pith-number/GRBVGW2I2VMJNIVTSEUZTD5UPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG/action/storage_attestation","attest_author":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG/action/author_attestation","sign_citation":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG/action/citation_signature","submit_replication":"https://pith.science/pith/GRBVGW2I2VMJNIVTSEUZTD5UPG/action/replication_record"}},"created_at":"2026-05-18T03:36:27.715166+00:00","updated_at":"2026-05-18T03:36:27.715166+00:00"}