Article contents
The critical Sobolev exponent in two dimensions
Published online by Cambridge University Press: 14 November 2011
Synopsis
The object of the paper is to investigate solutions of equations of the form
with
and in particular to look at the asymptotic behaviour of these solutions as γ ↑∞. It is found that, if tγ is the first zero of ϑ, then
while tγ is bounded below if p < 2. This answers questions raised by Brezis concerning solutions of −Δu = eup in R2
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 1-2 , 1988 , pp. 1 - 15
- Copyright
- Copyright © Royal Society of Edinburgh 1988
References
- 1
- Cited by