This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of trajectories featuring the weighted sum of energetic and dissipative terms. As the parameter ε is sent to 0, the minimizers of such functionals converge, up to subsequences, to curves of maximal slope driven by the functional ϕ. This delivers a new and general variational approximation procedure, hence a new existence proof, for metric gradient flows. In addition, it provides a novel perspective towards relaxation.
Weighted Energy-Dissipation principle for gradient flows in metric spaces
Rossi R.;Savare G.;Segatti A.;Stefanelli U.
2019-01-01
Abstract
This paper develops the so-called Weighted Energy-Dissipation (WED) variational approach for the analysis of gradient flows in metric spaces. This focuses on the minimization of the parameter-dependent global-in-time functional of trajectories featuring the weighted sum of energetic and dissipative terms. As the parameter ε is sent to 0, the minimizers of such functionals converge, up to subsequences, to curves of maximal slope driven by the functional ϕ. This delivers a new and general variational approximation procedure, hence a new existence proof, for metric gradient flows. In addition, it provides a novel perspective towards relaxation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
