Reverse superposition estimates in Sobolev spaces

Van Schaftingen, Jean
(2022) Pure and Applied Functional Analysis — Vol. 7, n° 2, p. 805-811 (2022)

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Abstract
We study when and how the norm of a function u in the homogeneous Sobolev spaces W˙s,p(Rn,Rm), with p≥1 and either s=1 or s>1/p, is controlled by the norm of composite function f∘u in the same space.
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Van Schaftingen, J. (2022). Reverse superposition estimates in Sobolev spaces. Pure and Applied Functional Analysis, 7(2), 805-811. https://hdl.handle.net/2078.5/246286 (Original work published 2022)