English

A partial boundary regularity and a regularity criterion for Harmonic Heat flow

Analysis of PDEs 2022-05-24 v1

Abstract

In my previous paper I have contrived a Ginzburg-Landau heat flow with a time-dependent parameter and by using it, I constructed a harmonic heat flow into spheres with a monotonical inequality and a reverse Poincar\'{e} inequality. This paper establishes these two energy inequalities near the boundary and then by making the best of them, we discuss a partial boundary regularity. In addition to it, we demonstrate a whole domain's regularity under "the one-sided condition." This has been proposed by S.Hildebrandt and K.-O.Widman.

Keywords

Cite

@article{arxiv.2205.10849,
  title  = {A partial boundary regularity and a regularity criterion for Harmonic Heat flow},
  author = {Kazuhiro Horihata},
  journal= {arXiv preprint arXiv:2205.10849},
  year   = {2022}
}
R2 v1 2026-06-24T11:24:48.024Z