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The critical Sobolev exponent in two dimensions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1988Publisher:Cambridge University Press (CUP)Journal:Proceedings of the Royal Society of Edinburgh: Section A Mathematics, volume 109, pages 1-15 (issn: 0308-2105, eissn: 1473-7124,

Authors: Bryce McLeod; Kevin McLeod;

doi: 10.1017/s0308210500026640

The critical Sobolev exponent in two dimensions

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Abstract

SynopsisThe object of the paper is to investigate solutions of equations of the formwithand 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, thenwhile tγ is bounded below if p < 2. This answers questions raised by Brezis concerning solutions of −Δu = eup in R2

Related Organizations

DePaul University
United States
University of Oxford
United Kingdom
University of Oxford
United Kingdom

Keywords

Asymptotic behavior of solutions to PDEs, asymptotics of radial solutions, Nonlinear elliptic equations

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