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Sobolev-Poincaré inequalities for p < 1

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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Official URL: http://www.iumj.indiana.edu/IUMJ/FULLTEXT/1994/43/...

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.
Subjects: Science & Engineering > Mathematics
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
URI:

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