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The annular decay property and capacity estimates for thin annuli
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1238-6751
University of Jyväskylä, Finland.
2017 (English)In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 68, no 2, 229-241 p.Article in journal (Refereed) Published
Abstract [en]

We obtain upper and lower bounds for the nonlinear variational capacity of thin annuli in weighted and in metric spaces, primarily under the assumptions of an annular decay property and a Poincar, inequality. In particular, if the measure has the 1-annular decay property at and the metric space supports a pointwise 1-Poincar, inequality at , then the upper and lower bounds are comparable and we get a two-sided estimate for thin annuli centred at . This generalizes the known estimate for the usual variational capacity in unweighted . We also characterize the 1-annular decay property and provide examples which illustrate the sharpness of our results.

Place, publisher, year, edition, pages
SPRINGER-VERLAG ITALIA SRL , 2017. Vol. 68, no 2, 229-241 p.
Keyword [en]
Annular decay property; Capacity; Doubling measure; Metric space; Newtonian space; Poincare inequality; Sobolev space; Thin annulus; Upper gradient; Variational capacity; Weighted R-n
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-137079DOI: 10.1007/s13348-016-0178-yISI: 000399158900004OAI: oai:DiVA.org:liu-137079DiVA: diva2:1093286
Note

Funding Agencies|Swedish Research Council; Academy of Finland [252108]; Vaisala Foundation of the Finnish Academy of Science and Letters

Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-05-05

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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