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Buckley, Stephen M. and Koskela, Pekka (1994) Sobolev-Poincaré inequalities for p < 1. Indiana University Mathematics Journal, 43 (1). pp. 221-240. ISSN 0022-2518
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Abstract
If Ω is a John domain (or certain more general domains), and |∇υ|a certain mild condition, we show that u Є W 1;1 loc (Ω) satisfies a Sobolev-Poincaré inequality (∫Ω|u – a|q)1/q ≤ C(∫Ω|∇u|p)1for all 0 < p < 1, and appropriate q > 0. Our conclusion is new even when is a ball.
| Item Type: | Article |
|---|---|
| Keywords: | Sobolev-Poincaré inequalities; John domain; Whitney decomposition; Lipschitz domain Ω. |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 1632 |
| Depositing User: | Prof. Stephen Buckley |
| Date Deposited: | 03 Nov 2009 10:43 |
| Journal or Publication Title: | Indiana University Mathematics Journal |
| Publisher: | Department of Mathematics Indiana University |
| Refereed: | No |
| Funders: | NSF Grant No. DMS-9207715, NSF Grant No. DMS-9305742 |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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