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Journal Articles Comptes Rendus. Mathématique Year : 2015

Superposition with subunitary powers in Sobolev spaces

Abstract

Let $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that the superposition operator $u\mapsto \Phi (u)$ maps the Sobolev space $W^{1,p}({\mathbb R}^n)$ into the fractional Sobolev space $W^{a,p/a}({\mathbb R}^n)$. We also investigate the case of more general nonlinearities.
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Dates and versions

hal-01069611 , version 1 (06-10-2014)
hal-01069611 , version 2 (15-10-2014)
hal-01069611 , version 3 (10-03-2015)

Identifiers

  • HAL Id : hal-01069611 , version 3

Cite

Petru Mironescu. Superposition with subunitary powers in Sobolev spaces. Comptes Rendus. Mathématique, 2015, 353 (6), pp.483--487. ⟨hal-01069611v3⟩
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