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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.03793","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-13T02:07:25Z","cross_cats_sorted":[],"title_canon_sha256":"bbae4c01045457f82713f9994d659f398e441545ee51e0350c3227cdc87dee46","abstract_canon_sha256":"71a5b12ba2201bd1d91f216eb5f14a0090e070616d775347bcaa3c2cfa2ece3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:10.707879Z","signature_b64":"jqOh0w3N46YlqipawUsu4hxk5E+PezI5rsl2dSK3QiOGBv+w8KtnWIsEM2LgtV9dt9Zifq5RwasPBUfiP+dSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c94594a0742b650c905bcbd8620106064ace0b5c5aff53d22c3774773a5db2f9","last_reissued_at":"2026-05-18T00:54:10.707482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:10.707482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $x=0$. 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