{"paper":{"title":"Matzoh ball soup revisited: the boundary regularity issue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","submitted_at":"2011-03-31T16:16:58Z","abstract_excerpt":"We consider nonlinear diffusion equations of the form $\\partial_t u= \\Delta \\phi(u)$ in $\\mathbb R^N$ with $N \\ge 2.$ When $\\phi(s) \\equiv s$, this is just the heat equation. Let $\\Omega$ be a domain in $\\mathbb R^N$, where $\\partial\\Omega$ is bounded and $\\partial\\Omega = \\partial (\\mathbb R^N\\setminus \\bar {\\Omega})$. We consider the initial-boundary value problem, where the initial value equals zero and the boundary value equals 1, and the Cauchy problem where the initial data is the characteristic function of the set $\\Omega^c = \\mathbb R^N\\setminus \\Omega$. We settle the boundary regulari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6229","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"}