44 citations · 135 across the 29 of their papers we have counts for
33 papers
Entropy and Fisher information in non-convex domains: one chain to rule them all
Jean-Baptiste Casteras, Marco Flaim, Léonard Monsaingeon
We prove that the (square root) Fisher information functional is a strong Wasserstein upper gradient of the entropy on non-convex Riemannian domains. This fills a gap in the litera…
A gradient flow that is none: Heat flow with Wentzell boundary condition
Marie Bormann, Léonard Monsaingeon, D. R. Michiel Renger +1
We establish a representation of the heat flow with Wentzell boundary conditions on smooth domains as gradient descent dynamics for the entropy in a suitably extended Otto manifold…
Large deviations for sticky-reflecting Brownian motion with boundary diffusion
Jean-Baptiste Casteras, Leonard Monsaingeon, Luca Nenna
We study a Schilder-type large deviation principle for sticky-reflected Brownian motion with boundary diffusion, both at the static and sample path level in the short-time limit. A…
Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach
Clément Cancès, Léonard Monsaingeon, Andrea Natale
We propose a fully discrete finite volume scheme for the standard Fokker-Planck equation. The space discretization relies on the well-known square-root approximation, which falls i…
Sticky-reflecting diffusion as a Wasserstein gradient flow
Jean-Baptiste Casteras, Léonard Monsaingeon, Filippo Santambrogio
In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functio…
Trivariate distribution of sticky Brownian motion
Jean-Baptiste Casteras, Léonard Monsaingeon
In this short note we derive a closed form for the trivariate distribution (position, local time at the origin, and positive occupation time) of the one-dimensional sticky Brownian…
Construction of 2-bubbles for the energy critical bi-harmonic Schrödinger equation
Jean-Baptiste Casteras, Ilkka Holopainen, Léonard Monsaingeon
We construct a blowing-up solution for the energy critical focusing biharmonic nonlinear Schrödinger equation in infinite time in dimension . Our solution is radially sym…
Hidden dissipation and convexity for Kimura equations
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper we establish a rigorous gradient flow structure for one-dimensional Kimura equations with respect to some Wasserstein-Shahshahani optimal transport geometry. This is…
Invariant measures and global well-posedness for a fractional Schrödinger equation with Moser-Trudinger type nonlinearity
Jean-Baptiste Casteras, Léonard Monsaingeon
In this paper, we construct invariant measures and global-in-time solutions for a fractional Schr\" odinger equation with a Moser-Trudinger type nonlinearity $$ i\partial_t u= (-Δ)…
Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps
Hugo Lavenant, Léonard Monsaingeon, Luca Tamanini +1
If is a harmonic map valued in a metric space and is a convex function, in the sense that it ge…
Schrödinger encounters Fisher and Rao: a survey
Léonard Monsaingeon, Dmitry Vorotnikov
In this short note we review the dynamical Schrödinger problem on the non-commutative Fisher-Rao space of positive semi-definite matrix-valued measures. The presentation is meant t…
A degenerate elliptic-parabolic system arising in competitive contaminant transport
Margarida Baía, Farid Bozorgnia, Léonard Monsaingeon +1
In this work we investigate a coupled system of degenerate and nonlinear partial differential equations governing the transport of reactive solutes in groundwater. We show that the…
The dynamical Schrödinger problem in abstract metric spaces
Léonard Monsaingeon, Luca Tamanini, Dmitry Vorotnikov
In this paper we introduce the dynamical Schrödinger problem on abstract metric spaces, defined for a wide class of entropy and Fisher information functionals. Under very mild assu…
The Schrödinger problem on the non-commutative Fisher-Rao space
Léonard Monsaingeon, Dmitry Vorotnikov
We present a self-contained and comprehensive study of the Fisher-Rao space of matrix-valued non-commutative probability measures, and of the related Hellinger space. Our non-commu…
A new transportation distance with bulk/interface interactions and flux penalization
Léonard Monsaingeon
We introduce and study a new optimal transport problem on a bounded domain , defined via a dynamical Benamou-Brenier formulation. The model handles differ…
Computing harmonic maps between Riemannian manifolds
Jonah Gaster, Brice Loustau, Léonard Monsaingeon
In the previous paper [GLM2018], we showed that the theory of harmonic maps between Riemannian manifolds may be discretized by introducing triangulations with vertex and edge weigh…
Gradient flow formulations of discrete and continuous evolutionary models: a unifying perspective
Fabio A. C. C. Chalub, Léonard Monsaingeon, Ana Margarida Ribeiro +1
We consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenera…
Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport
Aymeric Baradat, Léonard Monsaingeon
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schrödinger problem, Brenier's relaxed mo…
Computing discrete equivariant harmonic maps
Jonah Gaster, Brice Loustau, Léonard Monsaingeon
We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately,…
Simulation of multiphase porous media flows with minimizing movement and finite volume schemes
Clément Cancès, Thomas O. Gallouët, Maxime Laborde +1
The Wasserstein gradient flow structure of the PDE system governing multiphase flows in porous media was recently highlighted in [C. Cancès, T. O. Gallouët, and L. Monsaingeon, {\i…
An unbalanced Optimal Transport splitting scheme for general advection-reaction-diffusion problems
Thomas Gallouët, Maxime Laborde, Léonard Monsaingeon
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a construc…
Incompressible immiscible multiphase flows in porous media: a variational approach
Clément Cancès, Thomas Gallouët, Leonard Monsaingeon
We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measure…
A new multicomponent Poincaré-Beckner inequality
S. Kondratyev, L. Monsaingeon, D. Vorotnikov
We prove a new vectorial functional inequality of Poincaré-Beckner type. The inequality may be interpreted as an entropy-entropy production one for a gradient flow in the metric sp…
A fitness-driven cross-diffusion system from polulation dynamics as a gradient flow
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
We consider a fitness-driven model of dispersal of interacting populations, which was previously studied merely in the case . Based on some optimal transport distance rece…