Quasiopen and p-path open sets, and characterizations of quasicontinuity
Functional Analysis
2017-02-13 v1 Analysis of PDEs
Abstract
In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincar\'e inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous.
Keywords
Cite
@article{arxiv.1509.02326,
title = {Quasiopen and p-path open sets, and characterizations of quasicontinuity},
author = {Anders Björn and Jana Björn and Jan Malý},
journal= {arXiv preprint arXiv:1509.02326},
year = {2017}
}
Comments
17 pages