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To be more precise, let $b: [0,T]\\times{\\mathbb R}^d\\rightarrow{\\mathbb R}^d$ be Borel measurable, where $T>0$ is arbitrarily fixed. Consider $$X_t=x+\\int_0^tb(s,X_s)ds+W_t,\\quad t\\in[0,T], \\, x\\in{\\mathbb R}^d,$$ where $\\{W_t\\}_{t\\in[0,T]}$ is a $d$-dimensional standard Wiener process. If $b=b_1+b_2$ such that $b_1(T-\\cdot)\\in\\mathcal{C}_q^0((0,T];L^p({\\mathbb R}^d))$ with $2/q+d/p=1$ for $p,q\\ge1$ and $\\|b_1(T-"},"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":"1711.05058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-14T11:11:03Z","cross_cats_sorted":[],"title_canon_sha256":"03570527c0971e47c3f5ff36699f8c74d35fbf09b2d96ba686255314844f613e","abstract_canon_sha256":"9ee8f94b89aa0184a793a61fe5d13d52f492b55c02288285b0100247bbc41ce0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:34.886992Z","signature_b64":"KX4hRRiE/X8z8SiM2oBduaoVL+aXfGIEryH6c+ZfJycTzPoYwSgn2rFP7uQbaPtKKGMeQvGIgZ1Od9QrwtQ/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e69424a0a51b644f72f5904bf9639cb0278412dcf446a51fd2bcecb0c0fc2493","last_reissued_at":"2026-05-18T00:30:34.886281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:34.886281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On weak solutions of stochastic differential equations with sharp drift coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guangying Lv, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2017-11-14T11:11:03Z","abstract_excerpt":"We extend Krylov and R\\\"{o}ckner's result \\cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. 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