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|Title:||Combining solutions of semilinear partial differential equations in ℝn with critical sobolev exponent|
Scalar curvature equation
|Source:||Leung, M.C. (2004). Combining solutions of semilinear partial differential equations in ℝn with critical sobolev exponent. Communications in Partial Differential Equations 29 (5-6) : 763-784. ScholarBank@NUS Repository.|
|Abstract:||We consider a positive C2-function u in ℝn which is equal to two different spherical solutions respectively in two disjoint domains. u satisfies the equation Δu + n(n - 2)Ku n+2/n-2 = 0 in ℝn. By a result of Gidas, Ni and Nirenberg, K ≢ 1 in ℝn. In this paper we discuss lower bounds on supℝn |K - 1|. The estimates are applied to study blow-up solutions and interaction of bubbles.|
|Source Title:||Communications in Partial Differential Equations|
|Appears in Collections:||Staff Publications|
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