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The optimal transport problem aims at finding an optimal way to transport a given probability measure into another. In contrast to the well-known Monge––Kantorovich problem, the ramified optimal transportation problem aims at modeling a branching transport network by an optimal transport path...
We investigate fourth order Paneitz equations of critical growth in the case of n -dimensional closed conformally flat manifolds, n ≥≥ 5. Such equations arise from conformal geometry and are modelized on the Einstein case of the geometric equation describing the effects of conformal changes...
In this article we consider a system of eikonal equations with a Dirichlet boundary condition. We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient.
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