CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

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

  Published:2001-06-01
 Printed: Jun 2001
  • Man Chun Leung
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We construct unbounded positive $C^2$-solutions of the equation $\Delta u + K u^{(n + 2)/(n - 2)} = 0$ in $\R^n$ (equipped with Euclidean metric $g_o$) such that $K$ is bounded between two positive 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 fast or reasonably slow according to the constructions. By imposing natural conditions on $u$, we obtain growth estimate on the $L^{2n/(n-2)}$-norm of the solution and show that it has slow decay.
Keywords: positive solution, conformal scalar curvature equation, growth estimate positive solution, conformal scalar curvature equation, growth estimate
MSC Classifications: 35J60, 58G03 show english descriptions Nonlinear elliptic equations
unknown classification 58G03
35J60 - Nonlinear elliptic equations
58G03 - unknown classification 58G03
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/