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.


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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