Removable singularities for div v=f in weighted Lebesgue spaces
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
Julkaistu sarjassa
Indiana University Mathematics JournalPäivämäärä
2018Tekijänoikeudet
© the Authors & Indiana University, 2018
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.
Julkaisija
Indiana UniversityISSN Hae Julkaisufoorumista
0022-2518Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/26359842
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