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Journal of the London Mathematical Society 1999 59(2):607-619; doi:10.1112/S0024610799007267
© 1999 by London Mathematical Society
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© The London Mathematical Society

Estimates for Dirichlet Eigenfunctions

M. Van Den Berg and E. Bolthausen

School of Mathematics, University of Bristol University Walk, Bristol BS8 1TW M.vandenBerg{at}bristol.ac.uk
Institut für Angewandte Mathematik, Universität Zürich Winterthurer Straße 190, CH-8057 Zürich, Switzerland eb{at}amath.unizh.ch

Received 26 January 1996. Revision received 2 October 1996.

Estimates for the Dirichlet eigenfunctions near the boundary of an open, bounded set in euclidean space are obtained. It is assumed that the boundary satisfies a uniform capacitary density condition.


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