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Remarks on the pure critical exponent problem

Published online by Cambridge University Press:  17 April 2009

E.N. Dancer
E.N. Dancer
Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia
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Abstract

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In this paper, we use geometric and analytic methods to study the existence of positive solutions of the pure critical exponent problem with Dirichlet boundary conditions. In particular we prove that there is no solution for domains which are nearly star-shaped and we show that being conformal to a star-shaped domain does not characterise the domains for which the problem has no solution. We also answer some questions of Rodriguez et al.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 2 , October 1998 , pp. 333 - 344
Copyright
Copyright © Australian Mathematical Society 1998

References

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