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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: n m has bounded variation and f: m k is Lipschitz continuous.

MSC:
49Q15Geometric measure and integration theory, integral and normal currents (optimization)
26B30Absolutely continuous functions, functions of bounded variation (several real variables)
46G05Derivatives, etc. (functional analysis)
26B40Representation and superposition of functions of several real variables
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems