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A general chain rule for distributional derivatives. (English) Zbl 0685.49027
Summary: We prove a general chain rule for the distributional derivatives of the composite function \(v(x)=f(u(x))\), where u: \({\mathbb{R}}^ n\to {\mathbb{R}}^ m\) has bounded variation and f: \({\mathbb{R}}^ m\to {\mathbb{R}}^ k\) is Lipschitz continuous.

MSC:
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
26B30 Absolutely continuous real functions of several variables, functions of bounded variation
46G05 Derivatives of functions in infinite-dimensional spaces
26B40 Representation and superposition of functions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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