Abstract

In this note we deal with the problem of the density of smooth functions in weighted Sobolev spaces extending research of O. V. Besov ["On the denseness of the compactly supported functions in a weighted Sobolev space", Proc. Steklov Inst. Mat. 161 (1984) 33–52]. Using the common terminology we show in particular that if n=2n = 2, then for every p>1p > 1 the equality between W1,p(Ω,λ)W^{1,p}(\Omega, \lambda) and H1,p(Ω,λ)H^{1,p}(\Omega, \lambda) does not hold any more for a suitable weight λ\lambda.

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Valeria Chiadò Piat

Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, I-10129 Torino, Italy.

Francesco Serra Cassano

Dipartimento di Matematica, Università degli Studi di Trento, Via Sommarive 14, I-38050 Povo (Trento), Italy.

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Suggested citation

V. Chiadò Piat, F. Serra Cassano. “Some Remarks About the Density of Smooth Functions in Weighted Sobolev Spaces.” Journal of Convex Analysis 1 (1994), No. 2, 135–142. https://doi.org/10.68381/jca01010

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press.