13 citations · 33 across the 13 of their papers we have counts for
14 papers
Sharp local sparsity of regularized optimal transport
Alberto González-Sanz, Rishabh S. Gvalani, Lukas Koch
In recent years, the use of entropy-regularized optimal transport with -type entropies has become increasingly popular. In this setting, the solutions are sparse, in the sense…
On the Lavrentiev gap for convex, vectorial integral functionals
Lukas Koch, Matthias Ruf, Mathias Schäffner
We prove the absence of a Lavrentiev gap for vectorial integral functionals of the form $$ F: g+W_0^{1,1}(Ω)^m\to\mathbb{R}\cup\{+\infty\},\qquad F(u)=\int_ΩW(x,\mathrm{D} u)\,\mat…
Lecture notes on the harmonic approximation to quadratic optimal transport
Lukas Koch, Felix Otto
These lecture notes present the quantitative harmonic approximation result for quadratic optimal transport and general measures obtained by Goldman and Otto. The aim is to give a c…
Geometric linearisation for optimal transport with strongly p-convex cost
Lukas Koch
We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are…
Boundary regularity results for minimisers of convex functionals with -growth
Christopher Irving, Lukas Koch
We prove improved differentiability results for relaxed minimisers of vectorial convex functionals with -growth, satisfying a Hölder-growth condition in . We consider bo…
On global absence of Lavrentiev gap for functionals with (p,q)-growth
Lukas Koch
This pre-print has now been superseded by arXiv:2305.19934 and will not be published. We prove that for convex vectorial functionals with (p,q)-growth the Lavrentiev phenomenon doe…