location:  Publications → journals → CJM
Abstract view

# Monotonically Controlled Mappings

Published:2011-02-18
Printed: Apr 2011
• Libor Pavlíček,
Department of Mathematical Analysis, Charles University, Nečas Center for Mathematical Modeling, Prague, Czech Republic
 Format: HTML LaTeX MathJax PDF

## Abstract

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 Radó-Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the Fréchet 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, Radó-Reichelderfer property, UDM mapping, differentiability
 MSC Classifications: 26B05 - Continuity and differentiation questions 46G05 - Derivatives [See also 46T20, 58C20, 58C25]