Finsler structure for variable exponent Wasserstein space and gradient flows

In this paper, we propose a variational approach based on optimal transportation to study the existence and unicity of solution for a class of parabolic equations involving q(x)-Laplacian operator \begin{equation*}\label{equation variable q(x)} \frac{\partial \rho(t,x)}{\partial t}=div_x\left(\rho(t,x)|\nabla_x G^{'}(\rho(t,x))|^{q(x)-2}\nabla_x G^{'}(\rho(t,x)) \right) .\end{equation*} The variational approach requires the setting of new tools such as... Show more