{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:E27G2LRHRARRE3CPVOHCBFP3BZ","short_pith_number":"pith:E27G2LRH","schema_version":"1.0","canonical_sha256":"26be6d2e278823126c4fab8e2095fb0e60537bdbd61892bc304017224d1e86f8","source":{"kind":"arxiv","id":"1812.06358","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic behavior of the $W^{1/q,q}$-norm of mollified $BV$ functions and applications to singular perturbation problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Arkady Poliakovsky","submitted_at":"2018-12-15T21:18:20Z","abstract_excerpt":"Motivated by results of Figalli and Jerison and Hern\\'andez, we prove the following formula: \\begin{equation*} \\lim_{\\epsilon\\to 0^+}\\frac{1}{|\\ln{\\epsilon}|}\\big\\|\\eta_\\epsilon*u\\big\\|^q_{W^{1/q,q}(\\Omega)}= C_0\\int_{J_u}\\Big|u^+(x)-u^-(x)\\Big|^qd\\mathcal{H}^{N-1}(x), \\end{equation*} where $\\Omega\\subset\\mathbb{R}^N$ is a regular domain, $u\\in BV(\\Omega)\\cap L^\\infty$, $q>1$ and $\\eta_\\epsilon(z)=\\epsilon^{-N}\\eta(z/\\epsilon)$ is a smooth mollifier. In addition, we apply the above formula to the study of certain singular perturbation problems."},"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":"1812.06358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-15T21:18:20Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"50abc765c7c19cd00493e6efcd300439c61af77c5fc86de11b167a95172891cd","abstract_canon_sha256":"977de95e4889beb8a0b29b130403bfc2d3780eeb7960b432c267f544deda45b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:10.451940Z","signature_b64":"nop0sjAOisOqkbe58NCV4eUO3mlvo6d1tn4ycBYIsFrR/g7cTruzqvqhk1mEGbk+fVNiDNHXYfsqDzM/g38sCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26be6d2e278823126c4fab8e2095fb0e60537bdbd61892bc304017224d1e86f8","last_reissued_at":"2026-05-17T23:58:10.451394Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:10.451394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behavior of the $W^{1/q,q}$-norm of mollified $BV$ functions and applications to singular perturbation problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Arkady Poliakovsky","submitted_at":"2018-12-15T21:18:20Z","abstract_excerpt":"Motivated by results of Figalli and Jerison and Hern\\'andez, we prove the following formula: \\begin{equation*} \\lim_{\\epsilon\\to 0^+}\\frac{1}{|\\ln{\\epsilon}|}\\big\\|\\eta_\\epsilon*u\\big\\|^q_{W^{1/q,q}(\\Omega)}= C_0\\int_{J_u}\\Big|u^+(x)-u^-(x)\\Big|^qd\\mathcal{H}^{N-1}(x), \\end{equation*} where $\\Omega\\subset\\mathbb{R}^N$ is a regular domain, $u\\in BV(\\Omega)\\cap L^\\infty$, $q>1$ and $\\eta_\\epsilon(z)=\\epsilon^{-N}\\eta(z/\\epsilon)$ is a smooth mollifier. In addition, we apply the above formula to the study of certain singular perturbation problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06358","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":"1812.06358","created_at":"2026-05-17T23:58:10.451504+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.06358v1","created_at":"2026-05-17T23:58:10.451504+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.06358","created_at":"2026-05-17T23:58:10.451504+00:00"},{"alias_kind":"pith_short_12","alias_value":"E27G2LRHRARR","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"E27G2LRHRARRE3CP","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"E27G2LRH","created_at":"2026-05-18T12:32:19.392346+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/E27G2LRHRARRE3CPVOHCBFP3BZ","json":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ.json","graph_json":"https://pith.science/api/pith-number/E27G2LRHRARRE3CPVOHCBFP3BZ/graph.json","events_json":"https://pith.science/api/pith-number/E27G2LRHRARRE3CPVOHCBFP3BZ/events.json","paper":"https://pith.science/paper/E27G2LRH"},"agent_actions":{"view_html":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ","download_json":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ.json","view_paper":"https://pith.science/paper/E27G2LRH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.06358&json=true","fetch_graph":"https://pith.science/api/pith-number/E27G2LRHRARRE3CPVOHCBFP3BZ/graph.json","fetch_events":"https://pith.science/api/pith-number/E27G2LRHRARRE3CPVOHCBFP3BZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ/action/storage_attestation","attest_author":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ/action/author_attestation","sign_citation":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ/action/citation_signature","submit_replication":"https://pith.science/pith/E27G2LRHRARRE3CPVOHCBFP3BZ/action/replication_record"}},"created_at":"2026-05-17T23:58:10.451504+00:00","updated_at":"2026-05-17T23:58:10.451504+00:00"}