Calculus of Variations and Geometric Measure Theory
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G. Alberti - L. Ambrosio

A Geometrical Approach to Monotone Functions in ${\mathbb R}^n$

created on 22 May 1996
modified by alberti on 13 Mar 2016


Published Paper

Inserted: 22 may 1996
Last Updated: 13 mar 2016

Journal: Math. Zeit.
Volume: 230 (1999)
Pages: 259-316
Year: 1996


The paper is concerned with the fine properties of monotone maps on the n-dimensional Euclidean space. We study the continuity and the differentiability properties, compactness results, approximation by regular maps, structure of the distributional derivatives and of the distributional Jacobians. Among e exhibit an example of a continous monotone map which is the gradient of a convex function and whose distributional Jacobian is supported on a purely unrectifiable set.

Keywords: monotone functions, convex functions, current associated to the graph, distributional jacobian


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