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The Quarterly Journal of Mathematics 2004 55(3):267-302; doi:10.1093/qmath/hag050
© 2004 by Oxford University Press
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On the approximation numbers of Sobolev embeddings on singular domains and trees

W. D. Evans1, D. J. Harris1 and Y. Saito2

1 School of Mathematics, Cardiff University, 23 Senghennydd Road, Cardiff CF24 4YH 2 Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

Upper and lower bounds are determined for a function which counts the approximation numbers of the Sobolev embedding W1,p ({Omega})/C {rightarrowhook}Lp ({Omega})/C, for a wide class of domains {Omega} of finite volume in Rn and 1 < p < {infty}. Results on the distribution of the eigenvalues of the Neumann Laplacian in L2({Omega}) are special consequences.

Received 27 May 2003. Revised 12 November 2003.


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