Gradient flow structure for some nonlocal diffusion equations

Andrew Warren

We study ``nonlocal diffusion equations'' of the form \[ \partial_{t}\frac{dρ_{t}}{dπ}(x)+\int_{X}\left(\frac{dρ_{t}}{dπ}(x)-\frac{dρ_{t}}{dπ}(y)\right)η(x,y)dπ(y)=0\qquad(\dagger)…