Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps
نویسندگان
چکیده
منابع مشابه
Extension theorems for vector valued maps
We revisit studies on extension of Lipschitz maps and obtain new results about extension of displacements of bounded strain tensors. These questions are of interest in elasticity theory, optimal designs, as well as in functional analysis. Résumé Nous discutons l’extension d’applications Lipschitziennes et donnons, entre autres, une nouvelle démonstration d’un théorème de Schönbeck. Puis nous ét...
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We consider certain properties of maps of class C from R to Rd−1 that are strictly related to Sard’s theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give counterexamples showing that, in term of regularity, our results are optimal.
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We consider certain properties of maps of class C from R to Rd−1 that are strictly related to Sard’s theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give examples showing that, in term of regularity, our results are optimal.
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this contribution mainly focuses on some aspects of lipschitz groups, i.e., metrizable groups with lipschitz multiplication and inversion map. in the main result it is proved that metric groups, with a translation-invariant metric, may be characterized as particular group objects in the category of metric spaces and lipschitz maps. moreover, up to an adjustment of the metric, a...
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Sufficient conditions are given for a mapping to be γ -G inverse differentiable. Constrained implicit function theorems for γ -G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed subset. A theorem without assuming the γ -G inverse differentiability in a finite-dimensional space is also presented.
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2012
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-012-0189-0