We develop the notion of local fractional derivative introduced by Kolvankar and Gangal. It allows a fine study of the local structure of irregular (fractal) functions. Using this tool, we extend classical theorems of analysis (extrema, Rolle) to non-differentiable functions. In particular, we prove
Differentiability of minima of non-differentiable functionals
β Scribed by Mariano Giaquinta; Enrico Giusti
- Publisher
- Springer-Verlag
- Year
- 1983
- Tongue
- English
- Weight
- 497 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0020-9910
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π SIMILAR VOLUMES
## Abstract Let the Cantor set __C__ in β be defined by __C__ = βͺ^__r__^ ~__j__ =0~ __h~j~__ (__C__) with a disjoint union, where the __h~j~__ 's are similitude mappings with ratios 0 < __a~j~__ < 1. Let __ΞΌ__ be the selfβsimilar Borel probability measure on __C__ corresponding to the probability v
The aim of this paper is to define functions of several commuting and non-commuting self-adjoint pseudo-differential operators of non-positive order, by means of the H. Weyl formula Given 1<p< , the pseudo-differential operators under consideration belong to the Ho rmander class L m \, $ , m &n(1&\