A duality based approach to the minimizing total variation flow in the space $H^{-s}$

Yoshikazu Giga, Monika Muszkieta, Piotr Rybka

We consider a gradient flow of the total variation in a negative Sobolev space $H^{-s}$ $(0\le s\le 1)$ under the periodic boundary condition. If $s=0$, the flow is nothing but…