{"paper":{"title":"The regularity of the boundary of a multidimensional aggregation patch","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Bertozzi, Joan Verdera, John Garnett, Thomas Laurent","submitted_at":"2015-07-28T16:25:18Z","abstract_excerpt":"Let $d \\geq 2$ and let $N(y)$ be the fundamental solution of the Laplace equation in $R^d$ We consider the aggregation equation $$ \\frac{\\partial \\rho}{\\partial t} + \\operatorname{div}(\\rho v) =0, v = -\\nabla N * \\rho$$ with initial data $\\rho(x,0) = \\chi_{D_0}$, where $\\chi_{D_0}$ is the indicator function of a bounded domain $D_0 \\subset R^d.$ We now fix $0 < \\gamma < 1$ and take $D_0$ to be a bounded $C^{1+\\gamma}$ domain (a domain with smooth boundary of class $C^{1+\\gamma}$). Then we have Theorem: If $D_0$ is a $C^{1 + \\gamma}$ domain, then the initial value problem above has a solution g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07831","kind":"arxiv","version":2},"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"}