Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory. Abstract We obtain solutions of the nonlinear degenerate parabolic equation ∂ ρ ∂ t = div ρ ∇c ⋆ [ ∇ (F ′ (ρ) + V) ] as a steepest descent of an energy with respect to a convex cost functional. The method used here is variational. It requires less uniform convexity assumption than that imposed by Alt and ...

An analogue of the quadratic Wasserstein (or Monge-Kantorovich) distance between Borel probability measures on $\mathbf{R}^d$ has been defined in [F. Golse, C. Mouhot, T. Paul: Commun. Math. Phys. 343 (2015), 165-205] for density operators $L^2(\mathbf{R}^d)$, and used to estimate convergence rate various asymptotic theories context quantum mechanics. The present work proves a Kantorovich type ...

Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

We consider a variational optimization problem involving multifunctions and we prove a stability result with respect to the Monge-Kantorovich metric. We then show an application to variational problems defined on fractals generated by Iterated Function Systems.

In this paper, the numerical algorithm for solving the state and output feedback H∞-constrained LQG control problem is investigated. Although the equations that have to be solved to design the controller consist of the nonlinear crosscoupled algebraic Riccati equations (CAREs), it is newly proven that both the uniqueness and the positive semidefiniteness of the iterative solutions can be guaran...

Image registration is the process of establishing a common geometric reference frame between two or more data sets from the same or different imaging modalities possibly taken at different times. In the context of medical imaging and in particular image guided therapy, the registration problem consists of finding automated methods that align multiple data sets with each other and with the patie...