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# Extension Theorems on Weighted Sobolev Spaces and Some Applications

Published:2006-06-01
Printed: Jun 2006
• Seng-Kee Chua
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## Abstract

We extend the extension theorems to weighted Sobolev spaces $L^p_{w,k}(\mathcal D)$ on $(\varepsilon,\delta)$ domains with doubling weight $w$ that satisfies a Poincar\'e inequality and such that $w^{-1/p}$ is locally $L^{p'}$. We also make use of the main theorem to improve weighted Sobolev interpolation inequalities.
 Keywords: Poincaré inequalities, $A_p$ weights, doubling weights, $(\ep, \delta)$ domain, $(\ep, \infty)$ domain
 MSC Classifications: 46E35 - Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems