{"paper":{"title":"Regularity of the extremal solution for some elliptic problems with advection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Ye, Feng Zhou, Xue Luo","submitted_at":"2010-04-22T16:20:03Z","abstract_excerpt":"In this note, we investigate the regularity of extremal solution $u^*$ for semilinear elliptic equation $-\\triangle u+c(x)\\cdot\\nabla u=\\lambda f(u)$ on a bounded smooth domain of $\\mathbb{R}^n$ with Dirichlet boundary condition. Here $f$ is a positive nondecreasing convex function, exploding at a finite value $a\\in (0, \\infty)$. We show that the extremal solution is regular in low dimensional case. In particular, we prove that for the radial case, all extremal solution is regular in dimension two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3956","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"}