PDE Real Analysis Seminar

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2020/12/01

10:30-11:30   Room # Zoomによるオンライン開催  (Graduate School of Math. Sci. Bldg.)
Michał Łasica (Institute of Mathematics of the Polish Academy of Sciences / University of Tokyo)
Existence of the $1$-harmonic map flow (English)
[ Abstract ]
Similarly as in the real-valued case, the total variation of maps taking values in a Riemannian manifold extends to a lower semicontinuous functional on $L^2$. However, in general this functional is not geodesically semiconvex, so the existence of its gradient flow is not provided by general variational theory. Alternatively, one can try to apply the theory of parabolic PDE systems, mimicking the approach used for $p$-harmonic map flows, $p>1$. This poses some difficulties, because the PDE system corresponding to the flow is strongly nonlinear, singular and degenerate. However, in some cases, this approach was successful. In this talk, I will describe known results on the existence of the flow, focusing on my work with Lorenzo Giacomelli and Salvador Moll.