3 problems

Mean-convexity conjecture. If $\Gamma$ is strictly mean-convex near $F$, meaning that there is a positive constant $\gamma_0$ such that

Let $s\in(0,1]$ and let the initial data for the $H^{-s}$ total variation flow be Lipschitz. Instantaneous discontinuity conjecture. A solution may be instantaneously discontinuous…

Let $s\in[0,1]$ and consider the total variation flow in the space $H^{-s}$, namely the $(2s+2)$-order parabolic equation … with periodic boundary conditions and Lipschitz initial…