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Monotonically Controlled Mappings

Published online by Cambridge University Press:  20 November 2018

Libor Pavlíček*
Affiliation:
Department of Mathematical Analysis, Charles University, Nečas Center for Mathematical Modeling, Prague, Czech Republic email: [email protected]
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Abstract

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We study classes of mappings between finite and infinite dimensional Banach spaces that are monotone and mappings which are differences of monotone mappings ($\text{DM}$). We prove a Radó–Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for $\text{DM}$ mappings. This provides an alternative proof of the Fréchet differentiability a.e. of $\text{DM}$ mappings. We establish a Morrey-type estimate for the distributional derivative of monotone mappings. We prove that a locally $\text{DM}$ mapping between finite dimensional spaces is also globally $\text{DM}$. We introduce and study a new class of the so-called $\text{UDM}$ mappings between Banach spaces, which generalizes the concept of curves of finite variation.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2012

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