Let f be a Lipschitz map from a subset A of a stratified group to a Banach homogeneous group. We show that directional derivatives of f act as homogeneous homomorphisms at density points of A outside a σ-porous set. At all density points of A, we establish a pointwise characterization of differentiability in terms of directional derivatives. These results naturally lead us to an alternate proof of almost everywhere differentiability of Lipschitz maps from subsets of stratified groups to Banach homogeneous groups satisfying a suitably weakened Radon–Nikodym property.

Porosity and differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups / Magnani, V.; Pinamonti, A.; Speight, G.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 2020/199:(2020), pp. 1197-1220. [10.1007/s10231-019-00918-w]

Porosity and differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups

Magnani V.;Pinamonti A.;
2020-01-01

Abstract

Let f be a Lipschitz map from a subset A of a stratified group to a Banach homogeneous group. We show that directional derivatives of f act as homogeneous homomorphisms at density points of A outside a σ-porous set. At all density points of A, we establish a pointwise characterization of differentiability in terms of directional derivatives. These results naturally lead us to an alternate proof of almost everywhere differentiability of Lipschitz maps from subsets of stratified groups to Banach homogeneous groups satisfying a suitably weakened Radon–Nikodym property.
2020
Magnani, V.; Pinamonti, A.; Speight, G.
Porosity and differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups / Magnani, V.; Pinamonti, A.; Speight, G.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 2020/199:(2020), pp. 1197-1220. [10.1007/s10231-019-00918-w]
File in questo prodotto:
File Dimensione Formato  
Annali2.pdf

accesso aperto

Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 247.21 kB
Formato Adobe PDF
247.21 kB Adobe PDF Visualizza/Apri
Magnani2020_Article_PorosityAndDifferentiabilityOf.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 436.07 kB
Formato Adobe PDF
436.07 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/251555
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact