{"paper":{"title":"Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Panki Kim, Renming Song, Zhen-Qing Chen","submitted_at":"2010-11-15T00:47:20Z","abstract_excerpt":"Suppose that $d\\geq2$ and $\\alpha\\in(1,2)$. Let D be a bounded $C^{1,1}$ open set in $\\mathbb{R}^d$ and b an $\\mathbb{R}^d$-valued function on $\\mathbb{R}^d$ whose components are in a certain Kato class of the rotationally symmetric \\alpha-stable process. In this paper, we derive sharp two-sided heat kernel estimates for $\\mathcal{L}^b=\\Delta^{\\alpha/2}+b\\cdot\\nabla$ in D with zero exterior condition. We also obtain the boundary Harnack principle for $\\mathcal{L}^b$ in D with explicit decay rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3273","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"}