On the elliptic regularization of maximal slope curves

Abstract

We consider the so-called Weighted Energy-Dissipation approximation of gradient flows in metric spaces. We prove the convergence of minimizers to maximal slope curves under assumptions that are close to those of the original existence theory for metric gradient flows. The proof relies on an energy-dissipation identity for the approximating curves and on an adaptation of a general stability result for maximal slope curves.