Superposition operator in sobolev spaces on domains

Denis A. Labutin

doi:10.1090/s0002-9939-00-05421-6

Superposition operator in sobolev spaces on domains

Denis A. Labutin^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

For an arbitrary open set Ω ⊂ ℝⁿ we characterize all functions G on the real line such that G o u ∈ W^1,p(Ω) for all u ∈ W^1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W^1,p(Ω) → L^∞(Ω).

Original language	English
Pages (from-to)	3399-3403
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	128
Issue number	11
DOIs	https://doi.org/10.1090/s0002-9939-00-05421-6
Publication status	Published - 2000

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title = "Superposition operator in sobolev spaces on domains",

abstract = "For an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ W1,p(Ω) for all u ∈ W1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W1,p(Ω) → L∞(Ω).",

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AB - For an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ W1,p(Ω) for all u ∈ W1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W1,p(Ω) → L∞(Ω).

KW - Sobolev spaces

KW - Superposition operator

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U2 - 10.1090/s0002-9939-00-05421-6

DO - 10.1090/s0002-9939-00-05421-6

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VL - 128

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EP - 3403

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Superposition operator in sobolev spaces on domains

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