偏微分方程式セミナー(2016/12/2): Monotonicity type estimates and local regularity theorem for the p-harmonic map heat flows, 三沢 正史 氏 (熊本大学)

2016年 　 12月 2日 16時 30分 ～ 2016年 　 12月 2日 18時 00分

We study a geometric analysis for the evolutionary p-Laplace operator and show a local regularity theorem for the evolution of p-harmonic maps, called p-harmonic map heat flows. Our main result is to devise some new monotonicity type formulas of local scaled energy and establish a criterion for uniform local regularity estimate for regular p-harmonic map heat flows. The regularity criterion obtained is almost optimal, comparing with that of the corresponding stationary case. As application we show a compactness of regular p-harmonic map heat flows with energy bound.