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

2016122 16:30 
2016122 18:00
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Masashi Misawa (Kumamoto University)

 We study a geometric analysis for the evolutionary pLaplace operator and show a local regularity theorem for the evolution of pharmonic maps, called pharmonic 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 pharmonic 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 pharmonic map heat flows with energy bound.