We study the metric and -differentiability of pointwise Lipschitz mappings. First, we prove several theorems about metric and -differentiability of pointwise Lipschitz mappings between \( \Rn \) 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 <em>ω*</em>-Differentiability of Pointwise Lipschitz Mappings. Z. Anal. Anwend. 26 (2007), no. 3, pp. 341–362DOI 10.4171/ZAA/1328