Reverse approximation of gradient flows as Minimizing Movements: a conjecture by De Giorgi

Florentine Fleißner, Giuseppe Savaré

We consider the Cauchy problem for the gradient flow \begin{equation} \label{eq:81} \tag{$\star$} u'(t)=-\nablaϕ(u(t)),\quad t\ge 0;\quad u(0)=u_0, \end{equation} generated by a co…