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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 Poincaré inequalities, $A_p$ weights, doubling weights, $(\ep, \delta)$ domain, $(\ep, \infty)$ domain
MSC Classifications: 46E35 show english descriptions Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems 46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
 

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