Removable singularities for div v=f in weighted Lebesgue spaces
Abstract
Let w ∈ L
1
loc(R
n) be a positive weight. Assuming a doubling condition
and an L
1 Poincar´e inequality on balls for the measure w(x)dx, as well
as a growth condition on w, we prove that the compact subsets of R
n which are
removable for the distributional divergence in L∞
1/w are exactly those with vanishing
weighted Hausdorff measure. We also give such a characterization for L
p
1/w,
1 < p < +∞, in terms of capacity. This generalizes results due to Phuc and
Torres, Silhavy and the first author.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
Indiana University
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201805112536Use this for linking
Review status
Peer reviewed
ISSN
0022-2518
DOI
https://doi.org/10.1512/iumj.2018.67.6310
Language
English
Published in
Indiana University Mathematics Journal
Citation
- Moonens, L., Russ, E., & Tuominen, H. (2018). Removable singularities for div v=f in weighted Lebesgue spaces. Indiana University Mathematics Journal, 67(2), 859-887. https://doi.org/10.1512/iumj.2018.67.6310
License
Copyright© the Authors & Indiana University, 2018