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We then establish analogous results for reaction-diffusion equations such as \\eqref{e0} below in $\\Om \\times [0, T]$, where $\\Om$ is an epigraph such that the mean curvature of $\\partial \\Om$ is nonnegative.\n  We then turn our attention to settings where such gradient estimates are valid with"},"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":"1502.05758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T01:01:29Z","cross_cats_sorted":[],"title_canon_sha256":"e706ed3b1e4576846c93f72889a57ed13bcc8d3b3c704eda82c3506a2bc2cc22","abstract_canon_sha256":"66e70bcd88f1f7ce79fe0314c7b8c681fab74a2f9ac7cf8e99fc8aa9ef4b7bfb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:25.959162Z","signature_b64":"n8w4LKalYCj7UQxW9EEvUDpiRex0afv23hAii4myMVCVBjUZNl80aSiWxuGlA7Y3jeJtH3wP6rqdqacdREqiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"700df505f3fdd12715657859a5c6ad97b8c0af9ac139b5a44c90810b201a75c3","last_reissued_at":"2026-05-18T02:25:25.958665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:25.958665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modica type gradient estimates for reaction-diffusion equations and a parabolic counterpart of a conjecture of De Giorgi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Nicola Garofalo","submitted_at":"2015-02-20T01:01:29Z","abstract_excerpt":"We continue the study of Modica type gradient estimates for non-homogeneous parabolic equations initiated in \\cite{BG}. 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