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
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.
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