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On a class of Rellich inequalities

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
194
Issue
1
Identifiers
DOI: 10.1016/j.cam.2005.06.020
Keywords
  • Rellich Inequality
  • Best Constants
  • Distance Function
Disciplines
  • Mathematics

Abstract

Abstract 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.

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