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Extension Theorems on Weighted Sobolev Spaces and Some Applications

Published online by Cambridge University Press:  20 November 2018

Seng-Kee Chua
Seng-Kee Chua*
Affiliation:
National University of Singapore, Department of Mathematics 2, Science Drive 2 Singapore 117543matcsk@nus.edu.sg
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Abstract

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We extend the extension theorems to weighted Sobolev spaces $L_{w,k}^{p}\left( \mathcal{D} \right)$ on $(\varepsilon ,\delta )$ domains with doubling weight $w$ that satisfies a Poincaré 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

46E35Poincaré inequalitiesAp weightsdoubling weights(ε, δ) and (ε,∞) domains
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 3 , 01 June 2006 , pp. 492 - 528
Copyright
Copyright © Canadian Mathematical Society 2006

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