liu.seSearch for publications in DiVA
Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Dichotomy of global capacity density in metric measure spaces
Hokkaido Univ, Japan.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.ORCID-id: 0000-0002-9677-8321
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten.ORCID-id: 0000-0002-1238-6751
Univ Cincinnati, OH 45221 USA.
2018 (engelsk)Inngår i: Advances in Calculus of Variations, ISSN 1864-8258, E-ISSN 1864-8266, Vol. 11, nr 4, s. 387-404Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The variational capacity cap(p) in Euclidean spaces is known to enjoy the density dichotomy at large scales, namely that for every E subset of R-n, infx is an element of R(n)cap(p)(E boolean AND B(x, r), B(x, 2r))/cap(p)(B(x, r), B(x, 2r)) is either zero or tends to 1 as r -amp;gt; infinity. We prove that this property still holds in unbounded complete geodesic metric spaces equipped with a doubling measure supporting a p-Poincare inequality, but that it can fail in nongeodesic metric spaces and also for the Sobolev capacity in R-n. It turns out that the shape of balls impacts the validity of the density dichotomy. Even in more general metric spaces, we construct families of sets, such as John domains, for which the density dichotomy holds. Our arguments include an exact formula for the variational capacity of superlevel sets for capacitary potentials and a quantitative approximation from inside of the variational capacity.

sted, utgiver, år, opplag, sider
WALTER DE GRUYTER GMBH , 2018. Vol. 11, nr 4, s. 387-404
Emneord [en]
Capacitarily stable collection; capacitary potential; capacity density; dichotomy; metric space; Sobolev capacity; variational capacity
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-152075DOI: 10.1515/acv-2016-0066ISI: 000445862300004OAI: oai:DiVA.org:liu-152075DiVA, id: diva2:1258310
Merknad

Funding Agencies|JSPS KAKENHI [JP25287015, JP25610017, JP17H01092]; Swedish Research Council [621-2011-3139, 621-2014-3974, 2016-03424]; NSF [DMS-1200915, DMS-1500440]

Tilgjengelig fra: 2018-10-24 Laget: 2018-10-24 Sist oppdatert: 2018-10-24

Open Access i DiVA

Fulltekst mangler i DiVA

Andre lenker

Forlagets fulltekst

Søk i DiVA

Av forfatter/redaktør
Björn, AndersBjörn, Jana
Av organisasjonen
I samme tidsskrift
Advances in Calculus of Variations

Søk utenfor DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric

doi
urn-nbn
Totalt: 421 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf