The Weighted Energy Dissipation WED Principle for Gradient Flows

Explore the third part of a lecture series on the Weighted Energy Dissipation (WED) principle for gradient flows, presented by Giuseppe Savaré at the Hausdorff Center for Mathematics. Delve into an alternative variational method for constructing gradient flows in linear or metric spaces, focusing on a family of minimum problems for integral functionals defined in the space of continuous paths. Examine the method's correspondence to elliptic regularization in Hilbert spaces and its various applications. Compare the WED approach with the Minimizing Movement scheme, and investigate the relationships between optimal control problems and Hamilton-Jacobi equations. Learn about convergence results under different energy functional assumptions, based on collaborative research. Gain insights into this advanced topic in mathematical analysis, presented as part of the Hausdorff Trimester Program on Optimal Transportation and its Applications.