English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It is well known that sets of $p$-capacity zero are removable for bounded$p$-harmonic functions, but on metric spaces there are examples of removablesets of positive capacity. In this paper, we show that this can happen even onunweighted $\mathbf{R}^n$ when $n > p$, although only in very special cases. Acomplete characterization of removable singularities for bounded$\mathcal{A}$-harmonic functions on weighted $\mathbf{R}^n$, $n \ge 1$, is alsogiven, where the weight is $p$-admissible. The same characterization is alsoshown to hold for bounded quasiharmonic functions on weighted $\mathbf{R}^n$,$n \ge 2$, as well as on unweighted $\mathbf{R}$. For bounded$\mathcal{A}$-superharmonic functions and bounded quasisuperharmonic functionson weighted $\mathbf{R}^n$, $n \ge 2$, we show that relatively closed sets areremovable if and only if they have zero capacity.

Removable singularities for bounded $\mathcal{A}$-(super)harmonic and quasi(super)harmonic functions on weighted $\mathbf{R}^n$