Two nonlinear days in Urbino 2017.
Electron. J. Diff. Eqns., Conference 25 (2018), pp. 7785.
Differentiability versus approximate differentiability
Luigi D'Onofrio
Abstract:
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
email: donofrio@uniparthenope.it

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