{"paper":{"title":"An $L_p$-Lipschitz theory for parabolic equations with time measurable pseudo-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ildoo Kim","submitted_at":"2017-07-15T06:30:35Z","abstract_excerpt":"In this article we prove the existence and uniqueness of a (weak) solution $u$ in $L_p\\left((0,T) , \\Lambda_{\\gamma+m}\\right)$ to the Cauchy problem \\begin{align}\n  \\notag &\\frac{\\partial u}{\\partial t}(t,x)=\\psi(t,i\\nabla)u(t,x)+f(t,x),\\quad (t,x) \\in (0,T) \\times \\mathbf{R}^d\n  \\label{main eqn} & u(0,x)=0, \\end{align} where $d \\in \\mathbb{N}$, $p \\in (1,\\infty]$, $\\gamma,m \\in (0,\\infty)$, $\\Lambda_{\\gamma+m}$ is the Lipschitz space on $\\mathbf{R}^d$ whose order is $\\gamma+m$, $f \\in L_p\\left((0,T) , \\Lambda_{\\gamma} \\right)$, and $\\psi(t,i\\nabla)$ is a time measurable pseudo-differential op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04694","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"}