University of Birmingham > Talks@bham > Analysis seminar > Chain rule formula

Chain rule formula

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If you have a question about this talk, please contact José Cañizo.

A chain rule formula (fg)’(x)=f’(g(x))g’(x) is standard. However even if f and g are piece-wise linear maps between finite-dimensional spaces, this formula may be invalid at every x.

We present a uniform approach to the situation when f and g are Lipschitz functions between separable Banach spaces. We show that the chain rule formula does hold without any artificial assumptions, if derivatives are replaced by complete derivative assignments.

The idea behind these assignments is that the derivative of f is understood as defined only in the direction of a suitable “tangent subspace” (and so it exists at every point), but these tangent subspaces are chosen in such a way that for any g they contain the range of g’(x) for almost every x.

This is a joint work with D. Preiss.

This talk is part of the Analysis seminar series.

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