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
Copyright© The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License.