Existence of large singular solutions of conformal scalar curvature equations in S-n Academic Article

abstract

• We prove that every positive function in C1 (Cn), n 6, can be approximated in the C1 (Sn) norm by a positive function K C1 (Sn) such that the conformal scalar curvature equation -u + n(n - 2)/4 u = Kun+2/n-2 in Sn (0.1) has a weak positive solution u whose singular set consists of a single point. Moreover, we prove there does not exist an apriori bound on the rate at which such a solution u blows up at its singular point. Our results is in contrast to a result of Caffarelli, Gidas, and Spruck which states that Eq. (0.1) with K identicallly a positive constant in Sn, n 3, does not have a weak positive solution u whose singular set consists of a single point. 2005 Elsevier Ltd. All rights reserved.

authors

• Taliaferro, Steven

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

author list (cited authors)

• Taliaferro, S. D.

citation count

• 1

complete list of authors

• Taliaferro, SD

publication date

• January 2005

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Conformal Scalar Curvature Equation
• Isolated Singularity
• Singular Solution

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2004.12.002

start page

• 192

end page

• 216

volume

• 224

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jfa.2004.12.002