Monotonically Controlled Mappings

Pavlíček, Libor

Canadian journal of mathematics, Tome 63 (2011) no. 2, pp. 460-480

Résumé

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.

Détail

DOI : 10.4153/CJM-2011-004-0

Mots-clés : 26B05, 46G05, monotone mapping, DM mapping, Radó-Reichelderfer property, UDM mapping, differentiability

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