Growth Estimates on Positive Solutions of the Equation $Delta u+K u^{frac{n+2}{n-2}}=0$ in $R^n$

Canadian mathematical bulletin

关键词: positive solution;    conformal scalar curvature equation;    growth estimate;   

DOI  :  10.4153/CMB-2001-021-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We construct unbounded positive $C^2$-solutions of the equation$Delta u + K u^{(n + 2)/(n - 2)} = 0$ in $R^n$ (equippedwith Euclidean metric $g_o$) such that $K$ is bounded between twopositive numbers in $R^n$, the conformal metric $g=u^{4/(n-2)}g_o$is complete, and the volume growth of $g$ can be arbitrarily fastor reasonably slow according to the constructions. By imposing naturalconditions on $u$, we obtain growth estimate on the $L^{2n/(n-2)}$-normof the solution and show that it has slow decay.

【 授权许可】

Unknown