English

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}
}

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17 pages