Reverse superposition estimates in Sobolev spaces

Jean Van Schaftingen

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arXiv · 2007.01742

Reverse superposition estimates in Sobolev spaces

Jean Van Schaftingen

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Abstract

We study when and how the norm of a function $u$ in the homogeneous Sobolev spaces $\dot{W}^{s, p} (\mathbb{R}^n, \mathbb{R}^m)$, with $p \ge 1$ and either $s = 1$ or $s > 1/p$, is controlled by the norm of composite function $f \circ u$ in the same space.

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Jean Van Schaftingen. 2020-11-26. Reverse superposition estimates in Sobolev spaces. https://arxiv.org/abs/2007.01742

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