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To this end, we prove that the gradients satisfy a reverse H\\\"older inequality near the boun"},"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":"1802.09175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-26T06:14:04Z","cross_cats_sorted":[],"title_canon_sha256":"c7772e58ea7ac79a1ac4e441695096f97427288325b59ce241a17a1f342debec","abstract_canon_sha256":"22776b411f62e384506bfb441c5f882c408021d5a073085b007ed43e301517c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:34.501005Z","signature_b64":"qrysFN7X5vwoXt8K1OhinxpBa1ApoZOONvhUHtQrOgrcCQGaqHh29nSEcLwbtIXzFmQrhKTBUdeT1NAQGrAHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03f1a80206a2366c5f132790c416203268d870068c850dddcab2fc7cbfe88660","last_reissued_at":"2026-05-18T00:22:34.500392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:34.500392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interior and boundary higher integrability of very weak solutions for quasilinear parabolic equations with variable exponents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jehan Oh, Karthik Adimurthi, Sun-Sig Byun","submitted_at":"2018-02-26T06:14:04Z","abstract_excerpt":"We prove boundary higher integrability for the (spatial) gradient of \\emph{very weak} solutions of quasilinear parabolic equations of the form $$ \\left\\{\n  \\begin{array}{ll} u_t - div \\mathcal{A}(x,t,\\nabla u) = 0 &\\quad \\text{on} \\ \\Omega \\times (-T,T), \\\\ u = 0 &\\quad \\text{on} \\ \\partial \\Omega \\times (-T,T),\n  \\end{array} \\right. $$ where the non-linear structure $\\mathcal{A}(x, t,\\nabla u)$ is modelled after the variable exponent $p(x,t)$-Laplace operator given by $|\\nabla u|^{p(x,t)-2} \\nabla u$. 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