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A Generalization of an Inequality of Bhattacharya and Leonetti

Published online by Cambridge University Press:  20 November 2018

Ritva Hurri-Syrjänen
Ritva Hurri-Syrjänen*
Affiliation:
Department of Mathematics, University of Helsinki, P.O. Box 4 (Ylipistonhatu 5) FIN-00014, University of Helsinki, Finland e-mail: hurrisyrjane@cc.helsinki.fi
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Abstract

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We show that bounded John domains and bounded starshaped domains with respect to a point satisfy the following inequality

where F: [0, ∞) → [0, ∞) is a continuous, convex function with F(0) = 0, and u is a function from an appropriate Sobolev class. Constants b and K do depend at most on D. If F(x) = xp, 1 ≤ p < ∞, this inequality reduces to the ordinary Poincaré inequality.

Keywords

46E3526D10Poincaré-type inequalitiesJohn domainsstarshaped domains
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 438 - 447
Copyright
Copyright © Canadian Mathematical Society 1996

References

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