1. CJM 2011 (vol 63 pp. 460)
| Monotonically Controlled Mappings|
We study classes of mappings between finite and infinite dimensional Banach spaces that are monotone and mappings which are differences of monotone mappings (DM). We prove a RadÃ³-Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the FrÃ©chet differentiability a.e. of DM mappings. We establish a Morrey-type estimate for the distributional derivative of monotone mappings. We prove that a locally DM mapping between finite dimensional spaces is also globally DM. We introduce and study a new class of the so-called UDM mappings between Banach spaces, which generalizes the concept of curves of finite variation.
Keywords: monotone mapping, DM mapping, RadÃ³-Reichelderfer property, UDM mapping, differentiability