{"paper":{"title":"Green's function estimates for time fractional evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Ifan Johnston, Vassili Kolokoltsov","submitted_at":"2019-06-28T12:18:31Z","abstract_excerpt":"We look at estimates for the Green's function of time-fractional evolution equations of the form $D^{\\nu}_{0+*} u = Lu$, where $D^{\\nu}_{0+*}$ is a Caputo-type time-fractional derivative, depending on a L\\'evy kernel $\\nu$ with variable coefficients, which is comparable to $y^{-1-\\beta}$ for $\\beta \\in (0, 1)$, and $L$ is an operator acting on the spatial variable. First, we obtain global two-sided estimates for the Green's function of $D^{\\beta}_0 u = Lu$ in the case that $L$ is a second order elliptic operator in divergence form. Secondly, we obtain global upper bounds for the Green's functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12157","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"}