Estimates of best constants for weighted poincaré inequalities on convex domains

Proceedings of the London Mathematical Society

Volumn 93, Issue 1, 2006, Pages 197-226

  Chua, Seng Kee ^a   Wheeden, Richard L ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745041992     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1017/S0024611506015826     Document Type: Article

References (23)

1. 1 for convex domains', Proc. Amer. Math. Soc. 132 (2003) 195-202.
2. A. ADAMS and J. FOURNIES., Sobolev spaces (Academic Press, New York, 2003).
3. T. AUBIN, 'Problèmes isopérimétriques et espaces de Sobolev', J. Differential Geom. 11 (1976) 573-598.
4. M. BEBENDORF, 'A note on the Poincaré inequality for convex domains', Z. Anal. Anwendungen 22 (2003) 751-756.
5. B. BOJARSKI, 'Remarks on Sobolev imbedding inequalities', Complex analysis (ed. I. Laine and S. Rickman), Lecture Notes in Mathematics 1351 (Springer, New York, 1989) 52-68.
6. S.-K. CHUA, 'Extension theorems on weighted Sobolev spaces', Indiana. Math. J. 41 (1992) 1027-1076.
7. S.-K. CHUA, 'Weighted Sobolev's inequalities on domains satisfying the chain condition', Proc. Amer. Math. Soc. 117 (1993) 449-157.
8. S.-K. CHUA, 'On weighted Sobolev spaces', Cajiad. J. Math. 48 (1996) 527-541.
9. S.-K. CHUA and R. L. WHEEDEN, 'Sharp conditions for weighted 1-dimensional Poincaré inequalities', Indiana Math. J. 49 (2000) 143-175.
10. S.-K. CHUA and R. L. WHEEDEN, 'A note on sharp 1-dimensional Poincaré inequalities', Proc. Amer. Math. Soc. 134 (2006) 2309-2316.
11. A. CIANCHI, D. E. EDMUNDS and P. GURKA, 'On weighted Poincaré inequalities', Math. Nachr. 180 (1996) 15-41.
12. R. J. GARDNER, 'The Brunn-Minkowski inequality', Bull. Amer. Math. Soc. 39 (2002) 355-405.
13. P. GURKA and A. KUFNER, 'A note on a two-weighted Sobolev inequality', Approximation and function spaces (ed. Z. Ciesielski), Banach Center Publications 22 (Polish Academy of Science, Warsaw, 1989) 215-235.
14. K. HILDÉN, 'Symmetrization of functions in Sobolev spaces and the isopermetric inequality', Manuscripta Math. 18 (1976) 215-235.
15. P. JONES, 'Quasiconformal mappings and extendability of functions in Sobolev spaces', Acta Math. 147 (1981) 71-88.
16. A. KUFNER and B. OPIC, Hardy-type inequalities, Pitman Research Notes 219 (Longman, Harlow, UK, 1990).
17. E. H. LIEB, 'Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities', Ann. of Math. 18 (1983) 349-374.
18. G. LU and R. L. WHEEDEN, 'Poincaré inequalities, isoperimetric estimates and representation formulas on product spaces', Indiana Math. J. 47 (1998) 123-151.
19. V. G. MAZ'JA, Sobolev spaces (Springer, New York, 1985).
20. L. E. PAYNE and H. F. WEINBERGER, 'An optimal Poincaré inequality for convex domains', Arch. Rational Mech. Anal. 5 (1960) 286-292.
21. 2', SIAM. J. Appl. Math. 21 (1971) 30-32.
22. G. TALENTI, 'Best constant in Sobolev inequality', Ann. Mat. Pura Appl. 110 (1976) 353-372.
23. R. WEBSTER, Convexity (Oxford University Press, 1994).