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Global regularity and sparsity for regularised optimal transport
Xiaopeng Cheng, Lukas Koch, Haotian Xiao
We study regularised optimal transport with subquadratic or entropic regularisation. Under -assumptions on the marginals and the domains of their support, we prove global…
Sparsity and uniform regularity for regularised optimal transport
Rishabh S. Gvalani, Lukas Koch
We consider regularised quadratic optimal transport with subquadratic polynomial or entropic regularisation. In both cases, we prove interior Lipschitz-estimates on a transport-lik…
Uniform large-scale -regularity for entropic optimal transport
Rishabh S. Gvalani, Lukas Koch
We study the regularity properties of the minimisers of entropic optimal transport providing a natural analogue of the -regularity theory of quadratic optimal transpor…
Partial regularity for optimal transport with p-cost away from fixed points
Michael Goldman, Lukas Koch
We consider maps solving the optimal transport problem with a cost modeled on the -cost. For Hölder continuous marginals, we prove a -partial regularity re…
Quantified Legendreness and the regularity of minima
Cristiana De Filippis, Lukas Koch, Jan Kristensen
We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and -smoothness results for vector va…
On the validity of the Euler-Lagrange system without growth assumptions
Lukas Koch, Jan Kristensen
The constrained minimisers of convex integral functionals of the form defined on Sobolev mappings $v\in \mathrm W^{k,1}_g(Ω, \mat…