Local regularity and compactness for the p-harmonic map heat flows

摘要

We study a geometric analysis and local regularity forthe evolution of p {{p}} -harmonic maps, called p {{p}} -harmonic map heat flows.Our main result isto establish a criterion for a uniform local regularity estimatefor regular p {{p}} -harmonic map heat flows,devising some new monotonicity-type formulasof a local scaled energy.The regularity criterion obtained is almost optimal, comparing withthat of the corresponding stationary case.As application we show a compactness ofregular p {{p}} -harmonic map heat flows with energy bound.