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Finsler structure for variable exponent Wasserstein space and gradient flows

By Aboubacar Marcos and Ambroise Soglo
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
December 28, 2019
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Finsler structure for variable exponent Wasserstein space and gradient flows
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