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.
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}
}