arXiv subjects

F. -U. Caja-Lopez

Publications and source records attributed to F. -U. Caja-Lopez.

3 recordsLinked to original sources

arXiv2026

Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance

We establish several quantitative stability estimates for optimal transport maps between non-degenerate densities on uniformly convex domains for the quadratic cost. Under Hölder regularity assumptions, we prove Lipschitz $L^2$ (respectively $C^{1,α}$) stability estimates for optimal transport maps in terms of the 2-Monge-Kantorovich distance (respectively $L^{p}$ distances) between pairs of source and target densities. When the continuity assumption is removed, we obtain a Lipschitz $L^2$ stability estimate for the Brenier potentials in terms of the $L^2$ distance between the source and target densities. The proofs rely on a precise characterization of the linear response of the Brenier potential along smooth interpolations of the data, obtained by linearizing the Monge-Ampère equation in divergence form. As a further application of this approach, we derive an explicit formula for the second variation of the quadratic Monge-Kantorovich distance.

math.AP↗

arXiv2026

Uniqueness of bounded solutions to the fuzzy Landau and multiespecies Landau equations

We prove uniqueness of weak solutions to the fuzzy Landau equation and the multiespecies Landau system under suitable integrability assumptions. The results are based on explicit stability estimates in the 2-Wasserstein distance for a broader class of nonlinear equations with singular coefficients. Interestingly, this class includes the 2D incompressible Euler equations, the Vlasov-Poisson system, and the Patlak-Keller-Segel model, thereby recovering known uniqueness results within a unified framework. Our approach builds on the stochastic coupling method introduced by Fournier and Guerin for the homogeneous Landau equation, which we recast in a more analytic form. In addition, we present an alternative argument based on the symmetrization technique of Guillen and Silvestre, yielding comparable stability estimates.

math.AP↗

arXiv2025

Contractivity of Wasserstein distance and exponential decay for the Landau equation with Maxwellian molecules

Following the breakthrough work of Guillen and Silvestre \cite{GS24}, that shows that the Fisher information is monotonically decreasing for solutions to the homogeneous Landau equation, we study, for the same equation, the monotonicity properties of other physically relevant functionals. In the case of Maxwellian molecules, we show that the relative $L^2$ norm with respect to the equilibrium decays exponentially fast in time and is monotonically decreasing after some time. Moreover, still for the Maxwellian case, we provide a novel and short quantitative proof of time monotonicity of the entropic Wasserstein metric. For soft potentials, we show that the Wasserstein metric is contractive, conditional to $L^1(0,T,L^p(\mathbb{R}^3))$ bound for the solution. This result provides an alternative proof of the Fournier and Fournier-Guerin uniqueness theorem in \cite{fournier2009well_posedness_soft_potentials} \cite{fournier2010uniqueness_Coulomb}

math.AP↗