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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the limiting behavior of minimizing $p$-harmonic maps from a boundedLipschitz domain $\Omega \subset \mathbb{R}^{3}$ to a compact connectedRiemannian manifold without boundary and with finite fundamental group as $p\nearrow 2$. We prove that there exists a closed set $S_{*}$ of finite lengthsuch that minimizing $p$-harmonic maps converge to a locally minimizingharmonic map in $\Omega \setminus S_{*}$. We prove that locally inside $\Omega$the singular set $S_{*}$ is a finite union of straight line segments, and itminimizes the mass in the appropriate class of admissible chains. Furthermore,we establish local and global estimates for the limiting singular harmonic map.Under additional assumptions, we prove that globally in $\overline{\Omega}$ theset $S_{*}$ is a finite union of straight line segments, and it minimizes themass in the appropriate class of admissible chains, which is defined by a givenboundary datum and $\Omega$.

Limiting behavior of minimizing $p$-harmonic maps in 3d as $p$ goes to $2$ with finite fundamental group