This paper is concerned with the fine properties of monotone functions on $R^n$. We study the continuity and differentiability properties of these functions, the approximability properties, the structure of the distributional derivatives and of the weak Jacobians. Moreover, we exhibit an example of a monotone function $u$ which is the gradient of a $C^{1,\alpha}$ convex function and whose weak Jacobian $Ju$ is supported on a purely unrectifiable set.
A geometrical approach to monotone functions in R^n
ALBERTI, GIOVANNI;
1999-01-01
Abstract
This paper is concerned with the fine properties of monotone functions on $R^n$. We study the continuity and differentiability properties of these functions, the approximability properties, the structure of the distributional derivatives and of the weak Jacobians. Moreover, we exhibit an example of a monotone function $u$ which is the gradient of a $C^{1,\alpha}$ convex function and whose weak Jacobian $Ju$ is supported on a purely unrectifiable set.File in questo prodotto:
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