Výsledky vyhledávání - "46G05, 46T20"

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On $C^1$ Whitney extension theorem in Banach spaces

Our note is a complement to recent articles \cite{JS1} (2011) and \cite{JS2} (2013) by M. Jim\'enez-Sevilla and L. S\'anchez-Gonz\'alez which generalise (the basic statement of) the classical Whitney extension theorem for $C^1$-smooth real functions

Externí odkaz: http://arxiv.org/abs/2403.14317

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Universal Differentiability Sets in Carnot Groups of Arbitrarily High Step

Autor: Pinamonti, Andrea, Speight, Gareth

We show that every model filiform group $\mathbb{E}_{n}$ contains a measure zero set $N$ such that every Lipschitz map $f\colon \mathbb{E}_{n}\to \mathbb{R}$ is differentiable at some point of $N$. Model filiform groups are a class of Carnot groups w

Externí odkaz: http://arxiv.org/abs/1711.11433

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Universal differentiability sets and maximal directional derivatives in Carnot groups

Autor: Donne, Enrico Le, Pinamonti, Andrea, Speight, Gareth

Publikováno v: Journal de Math\'ematiques Pures et Appliqu\'ees 121 (2019), 83-112

We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some point of N. This relies on the fact that existence of a ma

Externí odkaz: http://arxiv.org/abs/1705.05871

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A Measure Zero Universal Differentiability Set in the Heisenberg Group

Autor: Pinamonti, Andrea, Speight, Gareth

We show that the Heisenberg group $\mathbb{H}^n$ contains a measure zero set $N$ such that every Lipschitz function $f\colon \mathbb{H}^n \to \mathbb{R}$ is Pansu differentiable at a point of $N$. The proof adapts the construction of small 'universal

Externí odkaz: http://arxiv.org/abs/1505.07986

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Differentiability of Lipschitz Functions in Lebesgue Null Sets

Autor: Preiss, David, Speight, Gareth

We show that if n>1 then there exists a Lebesgue null set in R^n containing a point of differentiability of each Lipschitz function mapping from R^n to R^(n-1); in combination with the work of others, this completes the investigation of when the clas

Externí odkaz: http://arxiv.org/abs/1304.6916

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Generalized differentiation with positively homogeneous maps: Applications in set-valued analysis and metric regularity

Autor: Pang, C. H. Jeffrey

We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and Lipschitz continu

Externí odkaz: http://arxiv.org/abs/0907.5439

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A compact null set containing a differentiability point of every Lipschitz function

Autor: Doré, Michael, Maleva, Olga

Publikováno v: Mathematische Annalen, Online First, 26 November 2010

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed

Externí odkaz: http://arxiv.org/abs/0804.4576

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