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On a class of Rellich inequalities

G. Barbatis·A. Tertikas
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Abstract

We prove Rellich and 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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G. Barbatis, A. Tertikas. 2004-12-07. On a class of Rellich inequalities. https://arxiv.org/abs/math/0412146

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