{"paper":{"title":"Dirichlet problem for supercritical nonlocal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Guohuan Zhao, Xicheng Zhang","submitted_at":"2018-09-15T13:20:49Z","abstract_excerpt":"Let $D$ be a bounded $C^2$-domain. Consider the following Dirichlet initial-boundary problem of nonlocal operators with a drift: $$ \\partial_t u={\\mathscr L}^{(\\alpha)}_\\kappa u+b\\cdot \\nabla u+f\\ \\mathrm{in}\\ \\mathbb R_+\\times D,\\ \\ u|_{\\mathbb R_+\\times D^c}=0,\\ u(0,\\cdot)|_{D}=\\varphi, $$ where $\\alpha\\in(0,2)$ and $\\mathscr L^{(\\alpha)}_\\kappa$ is an $\\alpha$-stable-like nonlocal operator with kernel function $\\kappa(x,z)$ bounded from above and below by positive constants, and $b:\\mathbb R^d\\to\\mathbb R^d$ is a bounded $C^\\beta$-function with $\\alpha+\\beta>1$, $f: \\mathbb R_+\\times D\\to\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05712","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"}