{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZQU4YRXCGYBSYHF4WLMCRDRGS2","short_pith_number":"pith:ZQU4YRXC","schema_version":"1.0","canonical_sha256":"cc29cc46e236032c1cbcb2d8288e2696a4a0f8a3f5b6fefa9755d5bdbf52d967","source":{"kind":"arxiv","id":"1310.4800","version":2},"attestation_state":"computed","paper":{"title":"A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Analia Silva, Juli\\'an Fern\\'andez Bonder, Nicolas Saintier","submitted_at":"2013-10-17T19:07:48Z","abstract_excerpt":"In this paper, we study the critical Sobolev embeddings $W^{1,p(x)}(\\Omega)\\subset L^{p^*(x)}(\\Omega)$ for variable exponent Sobolev spaces from the point of view of the $\\Gamma$-convergence. More precisely we determine the $\\Gamma$-limit of subcritical approximation of the best constant associated with this embedding. As an application we provide a sufficient condition for the existence of extremals for the best constant."},"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":"1310.4800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-17T19:07:48Z","cross_cats_sorted":[],"title_canon_sha256":"414102e10310ab91e358c16d905f35726348ea2562b32c90afbcde56092acadc","abstract_canon_sha256":"d640aa82b779334fbc6ca17c4f70309ca0bed4db4ac159ae262b11e3b9861d84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:32.797701Z","signature_b64":"I7FLkaragj/++khKBuoecB7XVRPmsx73IlNPLUVgdgrDHgkYXwhrDORj9AXy3eesKWL7wLqJTJ8ZiLc2RaY5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc29cc46e236032c1cbcb2d8288e2696a4a0f8a3f5b6fefa9755d5bdbf52d967","last_reissued_at":"2026-05-18T03:09:32.797011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:32.797011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Analia Silva, Juli\\'an Fern\\'andez Bonder, Nicolas Saintier","submitted_at":"2013-10-17T19:07:48Z","abstract_excerpt":"In this paper, we study the critical Sobolev embeddings $W^{1,p(x)}(\\Omega)\\subset L^{p^*(x)}(\\Omega)$ for variable exponent Sobolev spaces from the point of view of the $\\Gamma$-convergence. More precisely we determine the $\\Gamma$-limit of subcritical approximation of the best constant associated with this embedding. As an application we provide a sufficient condition for the existence of extremals for the best constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4800","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":"1310.4800","created_at":"2026-05-18T03:09:32.797119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.4800v2","created_at":"2026-05-18T03:09:32.797119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4800","created_at":"2026-05-18T03:09:32.797119+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQU4YRXCGYBS","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQU4YRXCGYBSYHF4","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQU4YRXC","created_at":"2026-05-18T12:28:09.283467+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/ZQU4YRXCGYBSYHF4WLMCRDRGS2","json":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2.json","graph_json":"https://pith.science/api/pith-number/ZQU4YRXCGYBSYHF4WLMCRDRGS2/graph.json","events_json":"https://pith.science/api/pith-number/ZQU4YRXCGYBSYHF4WLMCRDRGS2/events.json","paper":"https://pith.science/paper/ZQU4YRXC"},"agent_actions":{"view_html":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2","download_json":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2.json","view_paper":"https://pith.science/paper/ZQU4YRXC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.4800&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQU4YRXCGYBSYHF4WLMCRDRGS2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQU4YRXCGYBSYHF4WLMCRDRGS2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2/action/storage_attestation","attest_author":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2/action/author_attestation","sign_citation":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2/action/citation_signature","submit_replication":"https://pith.science/pith/ZQU4YRXCGYBSYHF4WLMCRDRGS2/action/replication_record"}},"created_at":"2026-05-18T03:09:32.797119+00:00","updated_at":"2026-05-18T03:09:32.797119+00:00"}