Geometric properties of Sobolev mappings

Ronald Francis Gariepy

Vol. 47 (1973), No. 2, 427–433

DOI: 10.2140/pjm.1973.47.427

Abstract

If f is a mapping from an open k-cube in R^k 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