PDE Seminar (2016/12/02): Monotonicity type estimates and local regularity theorem for the p-harmonic map heat flows, Masashi Misawa (Kumamoto University)

2016-12-2 16:30 - 2016-12-2 18:00
Faculty of Science Building #3, Room 309
Masashi Misawa (Kumamoto University)
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.