{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TESTZHZXGBPRHPOM6OO6C4X7XL","short_pith_number":"pith:TESTZHZX","schema_version":"1.0","canonical_sha256":"99253c9f37305f13bdccf39de172ffbae8b63f253a78f9adbfbb86a7957ee8d1","source":{"kind":"arxiv","id":"1804.00534","version":3},"attestation_state":"computed","paper":{"title":"Nonlocal Harnack inequalities for nonlocal heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Yong-Cheol Kim","submitted_at":"2018-03-28T23:16:05Z","abstract_excerpt":"In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator $\\rL_K$ as follows; \\begin{equation*}\\begin{cases} \\rL_K u+\\pa_t u=0 &\\text{ in $\\Om\\times(-T,0]$ } u=g &\\text{ in $\\bigl((\\BR^n\\s\\Om)\\times (-T,0]\\bigr)\\cup\\bigl(\\Om\\times\\{t=-T\\}\\bigr)$ } \\end{cases}\\end{equation*} where $g\\in C(\\BR^n\\times [-T,0])\\cap L^{\\iy}(\\BR^n\\times(-T,0])$ and $\\,\\Om\\,$ is a bounded domain in $\\BR^n$ with Lipschitz boundary. Moreover, we get nonlocal parabolic weak Harnack inequalities of the"},"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":"1804.00534","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-28T23:16:05Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b201eaf3f151577ddc58ec9263d0446eb2e9b0a9859a05118d3acf3fb16d8412","abstract_canon_sha256":"fdc527c05c95e4d6d62bb857f5e5da118eecb17374a7c8271f660d95b0987603"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:17.570623Z","signature_b64":"8egVYIXEmobT5DVf+XtzGuuz9aXJp+WZEUv3/QJmhegsvI2mklp9RmHuDDcHbvFfKmK0ev3HKHsFiZNoCFPkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99253c9f37305f13bdccf39de172ffbae8b63f253a78f9adbfbb86a7957ee8d1","last_reissued_at":"2026-05-18T00:11:17.569937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:17.569937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlocal Harnack inequalities for nonlocal heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Yong-Cheol Kim","submitted_at":"2018-03-28T23:16:05Z","abstract_excerpt":"In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator $\\rL_K$ as follows; \\begin{equation*}\\begin{cases} \\rL_K u+\\pa_t u=0 &\\text{ in $\\Om\\times(-T,0]$ } u=g &\\text{ in $\\bigl((\\BR^n\\s\\Om)\\times (-T,0]\\bigr)\\cup\\bigl(\\Om\\times\\{t=-T\\}\\bigr)$ } \\end{cases}\\end{equation*} where $g\\in C(\\BR^n\\times [-T,0])\\cap L^{\\iy}(\\BR^n\\times(-T,0])$ and $\\,\\Om\\,$ is a bounded domain in $\\BR^n$ with Lipschitz boundary. 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