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| Title: | Growth estimates on positive solutions of the equation Δu + Kun+2/n-2 = 0 in ℝn | Authors: | Leung, M.C. | Issue Date: | Jun-2001 | Citation: | 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 | URI: | http://scholarbank.nus.edu.sg/handle/10635/103360 | ISSN: | 00084395 |
| Appears in Collections: | Staff Publications |
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