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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

1. Bhattacharya, T. and Leonetti, F., A new Poincaré inequality and its application to the regularity ofminimizers of integral functionah with nonstandard growth, Nonlinear Anal. 17(1991), 833–839.Google Scholar
2. Gehring, F. W. and Martio, O., Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn., Series A. I. Math. 10(1985), 203–219.Google Scholar
3. Hurri, R., Poincaré domains in R”, Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertationes 71(1988), 1—42.Google Scholar
4. Martio, O., John domains, bilipschitz balls and Poincaré inequality, Rev. Roumaine Math. Pures Appl. 33(1988), 107–112.Google Scholar
5. Maz'ya, V. G., Sobolev spaces, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1985.Google Scholar
6. Stein, E. M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New Jersey, 1970.Google Scholar