Exception Sets of Intrinsic and Piecewise Lipschitz Functions

Publikationen: Beitrag in FachzeitschriftArtikelForschung(peer-reviewed)

Autoren

Externe Organisationseinheiten

  • Universität Graz
  • Universität Rostock

Abstract

We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their exception sets where the Lipschitz property fails. The newly introduced notion of permeability describes sets which are natural exceptions for Lipschitz continuity in a well-defined sense. One of the main results states that continuous functions which are intrinsically Lipschitz continuous outside a permeable set are Lipschitz continuous on the whole domain with respect to the intrinsic metric. We provide examples of permeable sets in R d, which include Lipschitz submanifolds.

Details

OriginalspracheEnglisch
Aufsatznummer118
Seitenumfang19
FachzeitschriftThe journal of geometric analysis
Jahrgang32.2022
Ausgabenummer4
Frühes Online-Datum1 Feb. 2022
DOIs
StatusVeröffentlicht - Apr. 2022