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Monotonically Controlled Mappings
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- Journal:
- Canadian Journal of Mathematics / Volume 63 / Issue 2 / 01 April 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 460-480
- Print publication:
- 01 April 2011
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- Article
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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.
