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26-XX Real functions
26Bxx Functions of several variables
26B15 Integration: length, area, volume

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The area formula for $W^{1, n}$ -mappings

Jan Malý (1994)

Commentationes Mathematicae Universitatis Carolinae

Let $f$ be a mapping in the Sobolev space $W^{1, n} (Ω, 𝐑^{n})$ . Then the change of variables, or area formula holds for $f$ provided removing from counting into the multiplicity function the set where $f$ is not approximately Hölder continuous. This exceptional set has Hausdorff dimension zero.

The Lebesgue integral as a Riemann integral.

Gonzalez-Velasco, Enrique A. (1987)

International Journal of Mathematics and Mathematical Sciences

The length of a lemmiscate.

Elia, M., Angeli, M.T.Galizia (1984)

Publications de l'Institut Mathématique. Nouvelle Série

Currently displaying 1 – 3 of 3