Banachraum (Raum 643)

We study the mean curvature flow with given non-smooth forcing term. In 2011, Mugnai and Roeger showed a global existence of the weak solution via the phase field method. Generally, the most difficult part of the proof of the existence theorem is the estimates of the positive part of the discrepancy measure. In this talk, we explain a new modified Allen-Cahn equation which satisfies the non-positivity of the discrepancy measure, and we prove the existence of the weak solution for the mean curvature flow with forcing term in suitable Sobolev spaces.

Prof. Keisuke Takasao

Japan