{"paper":{"title":"Nonlocal Harnack inequalities for nonlocal heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Yong-Cheol Kim","submitted_at":"2018-03-28T23:16:05Z","abstract_excerpt":"In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator $\\rL_K$ as follows; \\begin{equation*}\\begin{cases} \\rL_K u+\\pa_t u=0 &\\text{ in $\\Om\\times(-T,0]$ } u=g &\\text{ in $\\bigl((\\BR^n\\s\\Om)\\times (-T,0]\\bigr)\\cup\\bigl(\\Om\\times\\{t=-T\\}\\bigr)$ } \\end{cases}\\end{equation*} where $g\\in C(\\BR^n\\times [-T,0])\\cap L^{\\iy}(\\BR^n\\times(-T,0])$ and $\\,\\Om\\,$ is a bounded domain in $\\BR^n$ with Lipschitz boundary. Moreover, we get nonlocal parabolic weak Harnack inequalities of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00534","kind":"arxiv","version":3},"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"}