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Motivated by the Moser's proof of the Harnack's inequality as well as Moser iteration type arguments in the regularity theory, we d"},"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":"1310.2275","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-08T20:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"0283b1d67021eace859b7c933da9e31f47fedc8fbea667755e91a451fe867153","abstract_canon_sha256":"40fd092fd0e3096b8402621bbd4eef6ec701ac6ad79550d8f2ac032752468213"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:01.224033Z","signature_b64":"FR7N/4qQ0h83F/AahYZhDl7ve+vHUtsj+NtMIt4iYY3oTpMtNZuwqx5fyb2LzMLTQEPzDEdZBKw6F6NU7c0jAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22ae26521d08ac671afb92dba8f100a0b295df0200ffd7b558c0e05e17ea60a4","last_reissued_at":"2026-05-18T01:35:01.223600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:01.223600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A pointwise inequality for the fourth order Lane-Emden equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Mostafa Fazly, Xingwang Xu","submitted_at":"2013-10-08T20:38:14Z","abstract_excerpt":"We prove that the following pointwise inequality holds\n  \\begin{equation*} -\\Delta u \\ge \\sqrt\\frac{2}{(p+1)-c_n} |x|^{\\frac{a}{2}} u^{\\frac{p+1}{2}} + \\frac{2}{n-4} \\frac{|\\nabla u|^2}{u} \\ \\ \\text{in}\\ \\ \\mathbb{R}^n\n  \\end{equation*}\n  where $c_n:=\\frac{8}{n(n-4)}$, for positive bounded solutions of the fourth order H\\'{e}non equation that is \\begin{equation*} \\Delta^2 u = |x|^a u^p \\ \\ \\ \\ \\text {in }\\ \\ \\mathbb{R}^n \\end{equation*} for some $a\\ge0$ and $p>1$. 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