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PERTURBATION OF DOMAIN: SINGULAR RIEMANNIAN METRICS

Published online by Cambridge University Press:  06 March 2002

C. MASON
C. MASON
Affiliation:
Department of Mathematics, King's College London, Strand, London WC2R 2LS cmason@mth.kcl.ac.uk
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Abstract

We study the Hardy inequality for a class of manifolds equipped with a singular metric that becomes infinite on the boundary; in particular, we study the best constant possible. One application of this constant has been to a certain type of domain perturbation. This technique is useful when the domain has an irregular boundary as is the case here. However, our first result shows that the class of manifolds considered has a Hardy constant that lies outside the range permitted by existing theorems. Yet we are still able to prove theorems which give information about the domain perturbation problem and, moreover, we set up a specific example which can be used to show that our results are the best possible.

2000 Mathematical Subject Classification: 35P99, 47A75,47B25,58J99.

Keywords

boundary decayLaplacianHardy inequalityspectral convergencesingular Riemannian metric
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 84 , Issue 2 , March 2002 , pp. 473 - 491
Copyright
2002 London Mathematical Society

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