{"paper":{"title":"Schauder's estimate for nonlocal kinetic equations and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Mingyan Wu, Xicheng Zhang, Zimo Hao","submitted_at":"2019-03-24T10:56:45Z","abstract_excerpt":"In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degenerate nonlocal equation in $\\mathbb R^{2d}$ with H\\\"older coefficients: $$ \\partial_tu=\\mathscr L^{(\\alpha)}_{\\kappa;{\\rm v}} u+b\\cdot\\nabla u+f,\\ u_0=0, $$ where $u=u(t,x,{\\rm v})$ and $\\mathscr L^{(\\alpha)}_{\\kappa;{\\rm v}}$ is a nonlocal $\\alpha$-stable-like operator with $\\alpha\\in(1,2)$ and kernel function $\\kappa$, which acts on the variable ${\\rm v}$. As an application, we show the strong well-posedness to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09967","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"}