A Note about Differentiability of Maps Defined on Convex Subsets of Banach Spaces That May Be Nowhere Dense
✍ Scribed by Adriano Montanaro; Diego Pigozzi
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 238 KB
- Volume
- 213
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
In connection with continuum mechanics there are physically meaningful choices of infinite-dimensional Banach spaces such that the domain of constitutive maps is Ž nowhere dense in them, as V. J. Mizel and C.-C. Wang Arch. Rational Mech.
. Anal. 23, 1996, 124᎐134 pointed out. Thus the usual differential calculus on open sets cannot be applied there. Here we give a differentiability notion for maps f defined on any convex subset of a Banach space that may be nowhere dense. When the domain of f is open, this notion coincides with the usual one. We give the definitions and prove the theorems related to first and higher order derivatives of f.