{"paper":{"title":"Green's function and infinite-time bubbling in the critical nonlinear heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carmen Cortazar, Manuel del Pino, Monica Musso","submitted_at":"2016-04-25T03:20:45Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\R^n$, $n\\ge 5$. We consider the semilinear heat equation at the critical Sobolev exponent $$ u_t = \\Delta u + u^{\\frac{n+2}{n-2}} \\inn \\Omega\\times (0,\\infty), \\quad u =0 \\onn \\pp\\Omega\\times (0,\\infty). $$\n  Let $G(x,y)$ be the Dirichlet Green's function of $-\\Delta$ in $\\Omega$ and $H(x,y)$ its regular part. Let $q_j\\in \\Omega$, $j=1,\\ldots,k$, be points such that the matrix $$\n  \\left [ \\begin{matrix} H(q_1, q_1) & -G(q_1,q_2) &\\cdots & -G(q_1, q_k) -G(q_1,q_2) & H(q_2,q_2) & -G(q_2,q_3) \\cdots & -G(q_3,q_k) \\vdots & & \\ddots& \\vdots -G(q_1,q_k) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07117","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"}