{"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 $\\alpha\\in (0, 2)$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1454","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}