TY - JOUR

T1 - Exception Sets of Intrinsic and Piecewise Lipschitz Functions

AU - Leobacher, Gunther

AU - Steinicke, Alexander

N1 - Publisher Copyright: © 2022, The Author(s).

PY - 2022/4

Y1 - 2022/4

N2 - 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.

AB - 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.

KW - Intrinsic metric

KW - Permeable sets

KW - Piecewise Lipschitz continuity

UR - http://www.scopus.com/inward/record.url?scp=85124067772&partnerID=8YFLogxK

U2 - 10.1007/s12220-021-00860-5

DO - 10.1007/s12220-021-00860-5

M3 - Article

VL - 32.2022

JO - The journal of geometric analysis

JF - The journal of geometric analysis

SN - 1050-6926

IS - 4

M1 - 118

ER -