Vol. 47, No. 2, 1973

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Geometric properties of Sobolev mappings

Ronald Francis Gariepy

Vol. 47 (1973), No. 2, 427–433
Abstract

If f is a mapping from an open k-cube in Rk into Rn, 2 k n, whose coordinate functions belong to appropriate Sobolev spaces, then the area of f is the integral with respect to k dimensional Hausdorff measure over Rn of a nonnegative integer valued multiplicity function.

Mathematical Subject Classification 2000
Primary: 49F20
Secondary: 28A75
Milestones
Received: 7 March 1972
Published: 1 August 1973
Authors
Ronald Francis Gariepy