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Displaying similar documents to “On regularity estimates for mappings between embedded manifolds”

Metric subregularity of order q and the solving of inclusions

Michaël Gaydu, Michel Geoffroy, Célia Jean-Alexis (2011)

Open Mathematics

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We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.

Some remarks about metric spaces, spherical mappings, functions and their derivatives.

Stephen Semmes (1996)

Publicacions Matemàtiques

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If p ∈ R, then we have the radial projection map from R {p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a function in terms of its gradient, which can then be used to derive Sobolev inequalities, etc. In...