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On a class of Rellich inequalities

We prove the Rellich and the improved Rellich inequalities that involve the distance function from a hypersurface of codimension k, under a certain geometric assumption. In case, the distance is taken from the boundary, that assumption is the convexity of the domain. We also discuss the best constan...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2006-09, Vol.194 (1), p.156-172
Main Authors: Barbatis, G., Tertikas, A.
Format: Article
Language:English
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Summary:We prove the Rellich and the improved Rellich inequalities that involve the distance function from a hypersurface of codimension k, under a certain geometric assumption. In case, the distance is taken from the boundary, that assumption is the convexity of the domain. We also discuss the best constant of these inequalities.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.06.020