{"paper":{"title":"Singular limits and properties of solutions of some degenerate elliptic and parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui, SungHoon Kim","submitted_at":"2016-06-13T02:07:25Z","abstract_excerpt":"Let $n\\geq 3$, $0\\le m<\\frac{n-2}{n}$, $\\rho_1>0$, $\\beta>\\beta_0^{(m)}=\\frac{m\\rho_1}{n-2-nm}$, $\\alpha_m=\\frac{2\\beta+\\rho_1}{1-m}$ and $\\alpha=2\\beta+\\rho_1$. For any $\\lambda>0$, we prove the uniqueness of radially symmetric solution $v^{(m)}$ of $\\La(v^m/m)+\\alpha_m v+\\beta x\\cdot\\nabla v=0$, $v>0$, in $\\R^n\\setminus\\{0\\}$ which satisfies $\\lim_{|x|\\to 0}|x|^{\\frac{\\alpha_m}{\\beta}}v^{(m)}(x)=\\lambda^{-\\frac{\\rho_1}{(1-m)\\beta}}$ and obtain higher order estimates of $v^{(m)}$ near the blow-up point $x=0$. We prove that as $m\\to 0^+$, $v^{(m)}$ converges uniformly in $C^2(K)$ for any compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03793","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"}