189 citations · 290 across the 7 of their papers we have counts for
10 papers
Dissipative solutions for viscoelastic phase separation with degenerate mobility: a dynamic transport approach
Moritz Immanuel Gau, Katharina Hopf, Matthias Liero
We study the convergence of minimising movement approximations to weak solutions of a fourth-order viscoelastic phase separation system with degenerate concave mobility. The underl…
Talagrand-type transport inequalities for path spaces over Carnot groups
Peter K. Friz, Helena Kremp, Vaios Laschos +2
We consider Talagrand-type transportation inequalities for the law of Brownian motion on Carnot groups. An important example is the lift of standard Brownian motion to the Brownian…
Dimension reduction for a coupled electro-elastic saddle-point problem at finite strains
Kateryna Buryachenko, Annegret Glitzky, Matthias Liero +1
We study the finite deformation of a thin, elastically heterogeneous sheet subject to electrostatic coupling. The interaction between mechanics and electrostatics is formulated as…
Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow
Matthias Liero, Alexander Mielke, Oliver Tse +1
This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellin…
Uniqueness and regularity of weak solutions of a drift-diffusion system for perovskite solar cells
Annegret Glitzky, Matthias Liero
We establish a novel uniqueness result for an instationary drift-diffusion model for perovskite solar cells. This model for vacancy-assisted charge transport uses Fermi--Dirac stat…
Finite-strain poro-visco-elasticity with degenerate mobility
Willem J. M. van Oosterhout, Matthias Liero
A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elast…
Fine properties of geodesics and geodesic -convexity for the Hellinger-Kantorovich distance
Matthias Liero, Alexander Mielke, Giuseppe Savaré
We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger--Kantorovich problem (HK), providing sufficient conditions for the solvabili…
Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves
Matthias Liero, Alexander Mielke, Giuseppe Savaré
We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the well-known Kantorovich-Wasserstein distance. The ne…
Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures
Matthias Liero, Alexander Mielke, Giuseppe Savaré
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite natur…
On microscopic origins of generalized gradient structures
Matthias Liero, Alexander Mielke, Mark A. Peletier +1
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadra…