Abstract
In connection with continuum mechanics there are physically meaningful choices of infinite-dimensional Banach spaces such that the domain of constitutive maps is nowhere dense in them, as4pointed out. Thus the usual differential calculus on open sets cannot be applied there. Here we give a differentiability notion for mapsfdefined on any convex subset of a Banach space that may be nowhere dense. When the domain offis open, this notion coincides with the usual one. We give the definitions and prove the theorems related to first and higher order derivatives off.
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