Metric and -Differentiability of Pointwise Lipschitz Mappings

  • Jakub Duda

    Weizmann Institute of Science, Rehovot, Israel

Abstract

We study the metric and -differentiability of pointwise Lipschitz mappings. First, we prove several theorems about metric and -differentiability of pointwise Lipschitz mappings between and a Banach space (which extend results due to Ambrosio, Kirchheim and others), then apply these to functions satisfying the spherical Rado–Reichelderfer condition, and to absolutely continuous functions of several variables with values in a Banach space. We also establish the area formula for pointwise Lipschitz functions, and for -absolutely continuous functions with values in Banach spaces. In the second part of this paper, we prove two theorems concerning metric and -differentiability of pointwise Lipschitz mappings where are Banach spaces with being separable (resp. separable and with separable).

Cite this article

Jakub Duda, Metric and -Differentiability of Pointwise Lipschitz Mappings. Z. Anal. Anwend. 26 (2007), no. 3, pp. 341–362

DOI 10.4171/ZAA/1328