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On Weighted Sobolev Spaces

Published online by Cambridge University Press:  20 November 2018

Seng-Kee Chua
Seng-Kee Chua*
Affiliation:
National University of Singapore Department of Mathematics 10, Kent Ridge Crescent Singapore 0511 email: e-mail: matesk@math.nus.sg
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Abstract

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We study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains 𝓓 when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the Muckenhoupt Ap class locally in 𝓓. Moreover, when the weights wi(x) are of the form dist(x, Mi)αi, αi∈ ℝ, Mi⊂ 𝓓 that are doubling, we are able to obtain some extension theorems on (ε, ∞) domains.

Keywords

46E35Poincaré inequalitiesAp weightspower weightsdoublinglocally Ap weights(ε, δ) and (ε, ∞) domains
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 3 , 01 June 1996 , pp. 527 - 541
Copyright
Copyright © Canadian Mathematical Society 1996

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