{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XFPAHY5NZVL2RNXLJSFJULJVVK","short_pith_number":"pith:XFPAHY5N","schema_version":"1.0","canonical_sha256":"b95e03e3adcd57a8b6eb4c8a9a2d35aaa0d8b95081ff73c9aafe93d338471b2d","source":{"kind":"arxiv","id":"1508.03402","version":3},"attestation_state":"computed","paper":{"title":"A counterexample to maximal $L_p$-regularity of the stochastic heat equation in polygons: the case $p>4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kyeong-Hun Kim","submitted_at":"2015-08-14T02:04:24Z","abstract_excerpt":"Let $D$ be a domain in $R^d$ and $u$ be the solution to the stochastic heat equation $$ du=\\Delta u dt+ g\\,dW_t, \\quad t>0, x\\in D, $$ with zero initial and boundary data. Here $W_t$ is a one-dimensional Wiener process on a probability space $\\Omega$. It has been proved (see below for references) that for any $p\\geq 2$ the inequality $$ \\|\\nabla u\\|_{L_p(\\Omega\\times [0,T]\\times D)} \\leq c \\|g\\|_{L_p(\\Omega\\times [0,T]\\times D)} $$ holds if $\\partial D\\in C^1$. In this note we prove that if $p>4$ then this inequality fails in any polygon in $R^2$ having an angle greater than or equal to $\\frac"},"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":"1508.03402","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2015-08-14T02:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"bb3011af500323723540ac6a55d55060359b55d43e6b540f5024860c44cf8bcc","abstract_canon_sha256":"55aea7b32a12909ba2e185cbf59c4943610bcedc8d981ef77f4b66843e853a50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:32.454114Z","signature_b64":"qTx9CqBUOb+Gde7MAUowzIHhkIxiAvisQ9DNaE+7zkDVkxKcy7BcjmWvL2MZcRv/WpKbX7SBYRlBQua+lS0UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b95e03e3adcd57a8b6eb4c8a9a2d35aaa0d8b95081ff73c9aafe93d338471b2d","last_reissued_at":"2026-05-18T01:15:32.453400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:32.453400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A counterexample to maximal $L_p$-regularity of the stochastic heat equation in polygons: the case $p>4$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kyeong-Hun Kim","submitted_at":"2015-08-14T02:04:24Z","abstract_excerpt":"Let $D$ be a domain in $R^d$ and $u$ be the solution to the stochastic heat equation $$ du=\\Delta u dt+ g\\,dW_t, \\quad t>0, x\\in D, $$ with zero initial and boundary data. Here $W_t$ is a one-dimensional Wiener process on a probability space $\\Omega$. It has been proved (see below for references) that for any $p\\geq 2$ the inequality $$ \\|\\nabla u\\|_{L_p(\\Omega\\times [0,T]\\times D)} \\leq c \\|g\\|_{L_p(\\Omega\\times [0,T]\\times D)} $$ holds if $\\partial D\\in C^1$. In this note we prove that if $p>4$ then this inequality fails in any polygon in $R^2$ having an angle greater than or equal to $\\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03402","kind":"arxiv","version":3},"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":"1508.03402","created_at":"2026-05-18T01:15:32.453514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.03402v3","created_at":"2026-05-18T01:15:32.453514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03402","created_at":"2026-05-18T01:15:32.453514+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFPAHY5NZVL2","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFPAHY5NZVL2RNXL","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFPAHY5N","created_at":"2026-05-18T12:29:50.041715+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/XFPAHY5NZVL2RNXLJSFJULJVVK","json":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK.json","graph_json":"https://pith.science/api/pith-number/XFPAHY5NZVL2RNXLJSFJULJVVK/graph.json","events_json":"https://pith.science/api/pith-number/XFPAHY5NZVL2RNXLJSFJULJVVK/events.json","paper":"https://pith.science/paper/XFPAHY5N"},"agent_actions":{"view_html":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK","download_json":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK.json","view_paper":"https://pith.science/paper/XFPAHY5N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.03402&json=true","fetch_graph":"https://pith.science/api/pith-number/XFPAHY5NZVL2RNXLJSFJULJVVK/graph.json","fetch_events":"https://pith.science/api/pith-number/XFPAHY5NZVL2RNXLJSFJULJVVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK/action/storage_attestation","attest_author":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK/action/author_attestation","sign_citation":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK/action/citation_signature","submit_replication":"https://pith.science/pith/XFPAHY5NZVL2RNXLJSFJULJVVK/action/replication_record"}},"created_at":"2026-05-18T01:15:32.453514+00:00","updated_at":"2026-05-18T01:15:32.453514+00:00"}