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 construct and analyze solutions to a regularized homogeneous $p$-harmonicmap flow equation for general $p \geq 2$. The homogeneous version of theproblem is new and features a monotonicity formula extending the one found byStruwe for $p = 2$; such a formula is not available for the nonhomogeneousequation. The construction itself is via a Ginzburg-Landau-type approximation\`a la Chen-Struwe, employing tools such as a Bochner-type formula and an$\varepsilon$-regularity theorem. We similarly obtain strong subsequentialconvergence of the approximations away from a concentration set with paraboliccodimension at least $p$. However, the quasilinear and non-divergence nature ofthe equation presents new obstacles that do not appear in the classical case $p= 2$, namely uniform-time existence for the approximating problem, and thus ourbasic existence result is stated conditionally.

A new $p$-harmonic map flow with Struwe monotonicity