{"paper":{"title":"Global heat kernel estimates for symmetric Markov processes dominated by stable-like processes in exterior $C^{1,\\eta}$ open sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kyung-Youn Kim","submitted_at":"2015-01-15T08:23:07Z","abstract_excerpt":"In this paper, we establish sharp two-sided heat kernel estimates for a large class of symmetric Markov processes in exterior $C^{1,\\eta}$ open sets for all $t> 0$. The processes are symmetric pure jump Markov processes with jumping kernel intensity $$\\kappa(x, y)\\psi(|x-y|)^{-1}|x-y|^{-d-\\alpha}$$ where $\\alpha\\in(0,2)$, $\\psi$ is an increasing function on $[ 0, \\infty)$ with $\\psi(r)=1$ on $0<r\\le 1$ and $c_1e^{c_2r^{\\beta}}\\le \\psi(r)\\le c_3e^{c_4r^{\\beta}}$ on $r>1$ for $\\beta\\in[0, \\infty]$. A symmetric function $\\kappa(x, y)$ is bounded by two positive constants and $|\\kappa(x, y)-\\kappa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03598","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"}