Global inversion for metrically regular mappings between Banach spaces

Gutú, Olivia

doi:10.1007/s13163-020-00380-w

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2022

2024

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Cited by 3 publications

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“…To this end, we will further extend the notion of pseudo-Jacobian to this setting. In particular, our results here extend and encompass the previous results of [14] and [15] (extending them to an infinite-dimensional setting) and those of [16] and [8] (extending them to a Finsler manifold setting). The contents of the paper are as follows.…”

Section: Introductionsupporting

confidence: 86%

Metric regularity, pseudo-Jacobians and global inversion theorems on Finsler manifolds

Gutú¹,

Jaramillo²,

Madiedo³

2022

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Our aim in this paper is to study the global invertibility of a locally Lipschitz map f : X → Y between (possibly infinite-dimensional) Finsler manifolds, stressing the connections with covering properties and metric regularity of f . To this end, we introduce a natural notion of pseudo-Jacobian Jf in this setting, as is a kind of set-valued differential object associated to f . By means of a suitable index, we study the relations between properties of pseudo-Jacobian Jf and local metric properties of the map f , which lead to conditions for f to be a covering map, and for f to be globally invertible. In particular, we obtain a version of Hadamard integral condition in this context.

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