Lagrangian mean curvature flow for entire Lipschitz graphs. II (Q368627)

The paper deals with longtime existence of smooth solutions to the fully nonlinear Lagrangian parabolic equation \[ \begin{cases}\frac{\partial u}{\partial t}=\sum\limits_{i=1}^n \arctan \lambda_i,\\ u(x,0)=u_0(x), \end{cases} \] where \(\lambda_i\), \(i=1,\dots ,n\), are the eigenvalues of \(D^2u\) and the initial data \(u_0\) is a locally \(C^{1,1}\)-smooth function satisfying either {\parindent=0.6cm\begin{itemize}\item[(1)] \(-(1+\eta)I_n \leq D^2 u_0\leq (1+\eta)I_n\) for some positive dimensional constant \(\eta,\) or \item[(2)] \(u_0\) is weakly convex everywhere, or \item[(3)] \(u_0\) verifies a large supercritical Lagrangian phase condition. \end{itemize}} For Part I see [the authors, Calc. Var. Partial Differ. Equ. 44, No. 1--2, 199--220 (2012; Zbl 1238.53039)].