Two nonlinear days in Urbino 2017. Electron. J. Diff. Eqns., Conference 25 (2018), pp. 77-85.

Differentiability versus approximate differentiability

Luigi D'Onofrio

One of the main tools in geometric function theory is the fact that the area formula is true for Lipschitz mapping; if f is differentiable a.e. (in the classic sense) then f can be exhausted up to a set of zero measure; the restriction of f, set by set, is Lipschitz [6, Theorem 3.18]. The aim of this survey is to clarify the regularity assumptions for a map to be differentiable a.e., and to give some auxiliary results when it is not, using the notion of approximate differentiability.

Published September 15, 2018.
Math Subject Classifications: 46E35.
Key Words: Sobolev homeomorphism; Lusin condition; approximate differentiability.

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Luigi D'Onofrio
University of Napoli "Parthenope", Italy

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