21 citations · 48 across the 8 of their papers we have counts for
11 papers
Partial regularity of optimal transport with Coulomb cost
Gero Friesecke, Tobias Ried
We prove that for two-marginal optimal transport with Coulomb cost on , the optimal map is a diffeomorphism outside a closed set of Lebesgue measure zero pr…
Large scale regularity and correlation length for almost length-minimizing random curves in the plane
Tobias Ried, Christian Wagner
We consider a model of random curves in the plane related to the large-scale behavior of the Random Field Ising Model (RFIM) at temperature zero in two space dimensions. Our work i…
On a variational problem related to the Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities
Thiago Carvalho Corso, Tobias Ried
We explicitly solve a variational problem related to upper bounds on the optimal constants in the Cwikel--Lieb--Rozenblum (CLR) and Lieb--Thirring (LT) inequalities, which has rece…
Domain branching in micromagnetism: scaling law for the global and local energies
Tobias Ried, Carlos Román
We study the occurrence of domain branching in a class of -dimensional sharp interface models featuring the competition between an interfacial energy and a non-local field e…
Variational methods for a singular SPDE yielding the universality of the magnetization ripple
Radu Ignat, Felix Otto, Tobias Ried +1
The magnetization ripple is a microstructure formed in thin ferromagnetic films. It can be described by minimizers of a nonconvex energy functional leading to a nonlocal and nonlin…
Variational approach to regularity of optimal transport maps: general cost functions
Felix Otto, Maxime Prod'homme, Tobias Ried
We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $…
Cwikel's bound reloaded
Dirk Hundertmark, Peer Kunstmann, Tobias Ried +1
There are a couple of proofs by now for the famous Cwikel--Lieb--Rozenblum (CLR) bound, which is a semiclassical bound on the number of bound states for a Schrödinger operator, pro…
Entropy decay for the Kac evolution
Federico Bonetto, Alissa Geisinger, Michael Loss +1
We consider solutions to the Kac master equation for initial conditions where particles are in a thermal equilibrium and particles are out of equilibrium. We show that…
Solitary waves in nonlocal NLS with dispersion averaged saturated nonlinearities
Dirk Hundertmark, Young-Ran Lee, Tobias Ried +1
A nonlinear Schrödinger equation (NLS) with dispersion averaged nonlinearity of saturated type is considered. Such a nonlocal NLS is of integro-differential type and it arises natu…
Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried +1
We study weak solutions of the homogeneous Boltzmann equation for Maxwellian molecules with a logarithmic singularity of the collision kernel for grazing collisions. Even though in…
Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried +1
It has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplacian. This has led to the hope that the homogenous Boltzman…