A non-compactness result on the fractional Yamabe problem in large dimensions
- Title
- A non-compactness result on the fractional Yamabe problem in large dimensions
- Author
- 김승혁
- Keywords
- Fractional Yamabe problem; Blow-up analysis
- Issue Date
- 2017-12
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v. 273, no. 12, page. 3759-3830
- Abstract
- Let (Xn+1, g(+)) be an (n + 1)-dimensional asymptotically hyperbolic manifold with conformal infinity (M-n, [(h) over cap]). The fractional Yamabe problem addresses to solve P-gamma[g(+), (h) over cap](u) = cu(n+2 gamma/n-2 gamma), u > 0 on M where c is an element of R and P-gamma[g(+) , (h) over cap] is the fractional conformal Laplacian whose principal symbol is the Laplace-Beltrami operator (-Delta)(gamma) on M. In this paper, we construct a metric on the half space X = R-+(n+1), which is conformally equivalent to the unit ball, for which the solution set of the fractional Yamabe equation is non -compact provided that n >= 24 for gamma is an element of (0, gamma*) and n >= 25 for gamma is an element of [gamma*,1) where gamma* is an element of (0,1) is a certain transition exponent. The value of gamma* turns out to be approximately 0.940197.
- URI
- https://www.sciencedirect.com/science/article/pii/S0022123617302896?via%3Dihubhttps://repository.hanyang.ac.kr/handle/20.500.11754/116675
- ISSN
- 0022-1236; 1096-0783
- DOI
- 10.1016/j.jfa.2017.07.011
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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