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math.AP2023★ 3 cited
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…
math.AP2023
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…
math.AP2023
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…