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arXiv · 2401.16987

The higher order chain rule in Sobolev spaces

Gérard Bourdaud
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Abstract

We establish the Fa\`a di Bruno formula, in the sense of almost everywhere equality, for derivatives of the composed function $f \circ g$, for all function $f : R \rightarrow R$ such that $f$ acts on $W^m_p(R^n)$ by composition, and all $g \in W^m_p(R^n)$.

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Gérard Bourdaud. 2024-01-30. The higher order chain rule in Sobolev spaces. https://arxiv.org/abs/2401.16987

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