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Superposition operator in Sobolev spaces on domains

Authors:	Denis A. Labutin

Affiliation:	Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra 0200, ACT, Australia

Abstract:	For an arbitrary open set $Omegasubset mathbb{R}^n$ we characterize all functions on the real line such that $Gcirc uin W^{1,p}(Omega)$ for all $uin W^{1,p}(Omega)$ . New element in the proof is based on Maz'ya's capacitary criterion for the imbedding ${W^{1,p}(Omega)hookrightarrow L^infty(Omega)}$ .

Keywords:	Sobolev spaces superposition operator

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