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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.

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)
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