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|Title:||Growth estimates on positive solutions of the equation Δu + Kun+2/n-2 = 0 in ℝn|
|Source:||Leung, M.C. (2001-06). Growth estimates on positive solutions of the equation Δu + Kun+2/n-2 = 0 in ℝn. Canadian Mathematical Bulletin 44 (2) : 210-222. ScholarBank@NUS Repository.|
|Abstract:||We construct unbounded positive C2-solutions of the equation Δu + Ku(n+2/(n-2) = 0 in ℝn (equipped with Euclidean metric go) such that K is bounded between two positive numbers in ℝn, the conformal metric g = g4/(n-2) go is complete, and the volume growth of g can be arbitrarily fast or reasonably slow according to the constructions. By imposing natural conditions on u, we obtain growth estimate on the L2n/(n-2)-norm of the solution and show that it has slow decay.|
|Source Title:||Canadian Mathematical Bulletin|
|Appears in Collections:||Staff Publications|
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