{"paper":{"title":"Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in $C^{1,\\eta}$ open sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kyung-Youn Kim, Panki Kim","submitted_at":"2014-02-19T13:47:10Z","abstract_excerpt":"In this paper, we study sharp Dirichlet heat kernel estimates for a large class of symmetric Markov processes in $C^{1,\\eta}$ open sets. The processes are symmetric pure jump Markov processes with jumping intensity $\\kappa(x,y) \\psi_1 (|x-y|)^{-1} |x-y|^{-d-\\alpha}$, where $\\alpha \\in (0,2)$. Here, $\\psi_1$ is an increasing function on $[ 0, \\infty )$, with $\\psi_1(r)=1$ on $0<r \\le 1$ and $c_1e^{c_2r^{\\beta}} \\le \\psi_1(r) \\le c_3 e^{c_4r^{\\beta}}$ on $r>1$ for $\\beta \\in [0,\\infty]$, and $ \\kappa( x, y)$ is a symmetric function confined between two positive constants, with $|\\kappa(x,y)-\\kap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4660","kind":"arxiv","version":1},"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"}