Karmanova, M. B. Area and coarea formulas for the mappings of Sobolev classes with values in a metric space. (Russian, English) Zbl 1164.46323 Sib. Mat. Zh. 48, No. 4, 778-788 (2007); translation in Sib. Math. J. 48, No. 4, 621-628 (2007). Summary: We prove the metric differentiability and approximate metric differentiability for some broad classes of mappings with values in a metric space, including Sobolev classes. By way of application, we derive some metric analogs of area and coarea formulas. Cited in 19 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations 52A38 Length, area, volume and convex sets (aspects of convex geometry) Keywords:metric space; metric differentiability; mapping of the Sobolev class; area formula; coarea formula PDFBibTeX XMLCite \textit{M. B. Karmanova}, Sib. Mat. Zh. 48, No. 4, 778--788 (2007; Zbl 1164.46323); translation in Sib. Math. J. 48, No. 4, 621--628 (2007) Full Text: EuDML EMIS