Calculus of Variations and Geometric Measure Theory

T. Caillet - F. Santambrogio

Doubly nonlinear diffusive PDEs: new existence results via generalized Wasserstein gradient flows

created by santambro on 03 Feb 2024



Inserted: 3 feb 2024
Last Updated: 3 feb 2024

Year: 2024


We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an EDI formulation of our PDE and prove that under some integrability assumptions on the initial condition the PDE is satisfied in the sense of distributions.