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In this paper, by using probabilistic methods, we establish sharp two-sided pointwise estimates for the Dirichlet heat kernels of $\\{\\Delta+ a^\\alpha \\Delta^{\\alpha/2}; \\ a\\in (0, 1]\\}$ on half-space-like $C^{1, 1}$ domains in ${\\mathbb R}^d$ for all time $t>0$. The large time estimates for half-space-like domains are very different from those for bounded domains. Our estimates are uniform in $a \\in (0, 1]$ in the sense that the constants in the estimates are independent of $a\\in (0, 1]$. Thus it yields the Dirichlet heat kernel estimates for Brown"},"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":"1102.1454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-07T22:17:38Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"e49ab7736e803b1efc2c132c338e193e8d99d5016964a4489014e54efff04b89","abstract_canon_sha256":"3f0fbcef67e88673b2571c0683cf2ab016084055ef6566c2168fd0454c666898"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:57.788874Z","signature_b64":"cV0Nt0RVcnEoBMp5ZMtuAy0pPT1zaNwMRphiFFkerfbgA2SQQ1+IGb3kDl49n4JbN4HVS7OMYE3AC4wikcEEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8160d12b9863883da639f726078ddca68e8c39e58150da6f7183945ae327383c","last_reissued_at":"2026-05-18T04:27:57.788287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:57.788287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Heat Kernel Estimates for $\\Delta+\\Delta^{\\alpha/2}$ in Half-space-like domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Panki Kim, Renming Song, Zhen-Qing Chen","submitted_at":"2011-02-07T22:17:38Z","abstract_excerpt":"Suppose that $d\\ge 1$ and $\\alpha\\in (0, 2)$. 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