Inserted: 22 may 1996
Last Updated: 13 mar 2016
Journal: Math. Zeit.
Volume: 230 (1999)
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