Lorenzo Giacomelli, Michał Łasica
Published 2018-06-06Version 1
If $\boldsymbol u \colon [0, \infty[\times I \to \mathbb R^n$ is the solution to the total variation flow on an interval $I$ with initial datum $\boldsymbol u_0 \in BV(I, \mathbb R^n)$, then $|\boldsymbol u_x(t, \cdot)| \leq |\boldsymbol u_{0,x}|$ in the sense of measures on $I$ for $t>0$.
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