A discontinuous Sobolev function exists

Przemysław Górka , Artur Słabuszewski

Abstract

We prove that there always exist discontinuous functions in the Hajlasz-Sobolev space M 1,s on an s-Ahlfors regular metric space when s > 1. In this way an affirmative answer to the conjecture formulated by X. Zhou (2017) is given
Author Przemysław Górka (FMIS / DPDE)
Przemysław Górka,,
- Department of Partial Differential Equations
, Artur Słabuszewski (FMIS)
Artur Słabuszewski,,
- Faculty of Mathematics and Information Science
Journal seriesProceedings of the American Mathematical Society, ISSN 0002-9939, (N/A 100 pkt)
Issue year2019
Vol147
No2
Pages637-639
Publication size in sheets0.3
Keywords in Polishprzestrzenie Sobolewa, przestrzeń metryczna z miarą, miary Ahlforsa
Keywords in EnglishSobolev spaces, metric measure spaces, Ahlfors measure
ASJC Classification2604 Applied Mathematics; 2600 General Mathematics
Abstract in PolishWykazujemy, że w przestrzenie Hajłasza Sobolewa M^1,s na s regularnej przestrzenie Ahlforsa zawsze istnieje funkcja nieciągła. Tym samym udzielamy pozytywnej odpowiedzi na hipotezę Zhou.
DOIDOI:10.1090/proc/14164
URL http://www.ams.org/journals/proc/2019-147-02/S0002-9939-2018-14164-7/home.html
Languageen angielski
Score (nominal)100
Score sourcejournalList
ScoreMinisterial score = 100.0, 20-10-2019, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.984; WoS Impact Factor: 2017 = 0.707 (2) - 2017=0.726 (5)
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