Sharp capacity estimates for annuli in weighted R^n and in metric spaces

Abstract
We obtain estimates for the nonlinear variational capacity of annuli in weighted Rn and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted Rn. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted Rn, which are based on quasiconformality of radial stretchings in Rn.
Main Authors
Format
Articles Research article
Published
2017
Series
Subjects
Publication in research information system
Publisher
Springer Berlin Heidelberg
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201707203338Use this for linking
Review status
Peer reviewed
ISSN
0025-5874
DOI
https://doi.org/10.1007/s00209-016-1797-4
Language
English
Published in
Mathematische Zeitschrift
Citation
  • Björn, A., Björn, J., & Lehrbäck, J. (2017). Sharp capacity estimates for annuli in weighted R^n and in metric spaces. Mathematische Zeitschrift, 286(3-4), 1173- 1215. https://doi.org/10.1007/s00209-016-1797-4
License
Open Access
Copyright© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License.

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