Abstract
In this paper, superposition operators, $ (N_gu ) (x )= g (u (x ) )$, between two arbitrary Sobolev spaces are studied. Sufficient conditions which ensure the well-definedness, the continuity, and the validity of the higher-order chain rule for such operators are given in the subcritical case (see Remark 1.1). As a consequence of these properties, it is proved that $N_g (W^{m,p} (\Omega )\cap W_0^{k,p} (\Omega ) )\subset W_0^{l,q} (\Omega )$.
Citation
George Dinca. Florin Isaia. "On superposition operators between higher-order Sobolev spaces and a multivariate Faà di Bruno formula: the subcritical case." Differential Integral Equations 26 (1/2) 11 - 58, January/February 2013. https://doi.org/10.57262/die/1355867505
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